Draft tube

Application Challenge 6-07 © copyright ERCOFTAC 2004

CFD Simulations

Overview of CFD Simulations

Two international workshops, focused on this test case, have been organised: Turbine-99 - Workshop on Draft Tube Flow, Porjus, Sweden, 20-23 June 1999 (for Proceedings see Gebart et al., 2000a, hereafter in the text called Proc.T99W1), and Turbine-99 - Workshop 2 on Draft Tube Flows, Älvkarleby, Sweden, June 18-20, 2001 (for Proceedings see Engström et al. 2003, http://www.sirius.luth.se/strl/Turbine-99/index.htm (bad link, DCE 10-03-10), hereafter in the text called Proc.T99W2)). Brief summaries of the workshops have also been presented at the 20^th and 21^st IAHR Symposia on Hydraulic Machinery and Systems in Charlotte, N.C. 2000 (Gebart et al., 2000b), and in Lausanne, respectively, (Engström et al., 2002).

The first workshop was organised as a blind test and attracted 18 participants who contributed with comparison data and papers to the proceedings. The geometry and the axial and tangential velocity components at the inlet section were specified, while most of the remaining options were left to the participants to decide upon, e.g. grid and radial velocity component at the inlet. The focus was from an engineering point of view, to get an understanding of the difficulties of CFD-simulations and possible variations between different CFD-simulations of the test case. The first workshop showed that the case was very sensitive to different settings and the resulting C_p varied with up to ± 50 %. The reasons were as stated above: the choice of inlet boundary condition for the radial velocity had a large effect on the pressure recovery, many solutions were obtained on very coarse grid, various turbulence models were used, etc. To summarize: most of the computations were not performed according to the ERCOFTAC Best Practice Guidelines for Quality and Trust in Industrial CFD, which formally came out in the beginning of 2000 (Casey and Wintergerste, editors, 2000). Detailed results from the first workshop are available from Luleå University of Technology, Div. of Fluid Mechanics, see Proc.T99W1, Gebart et al (2000a). Since these results to a large extent are superseded by the results from the second workshop, we will not further discuss the results from the first workshop.

The second workshop focused more on quality and it was recommended to use the ERCOFTAC Best Practice Guidelines (Casey and Wintergerste, 2000) as a guide when performing computations. For this workshop the grid, the radial velocity component, turbulence model etc were specified for one test case, (case T), to get a reference solution from every participant in order to reduce the spread between the calculations. And for the 12 participants the variation in Cp_r was reduced to ± 20 %. Engström et al. 2001, Engström et al., 2003. The difference was still very big based on Cp_r wall, considering that all affecting variables should be the same. If one instead looks at Cp_rmean the difference is only ± 7 %.

In this document a brief comparison between the CFD-simulations will be given to demonstrate the agreement and differences between CFD results and experiments, with focus on the results from the second workshop. Results regarding engineering quantities (of which many are exactly the design or assessment parameters, DOAPs, defined for the test case) will be given for computations by all participants. A typical simulation of the standard test case T is then chosen to enable more detailed comparisons with the experiments.

The participating groups and their acronyms are given in Table 3.1

Table 3.1. List of acronyms

Acronym	Authors	Affiliation	CFD code
AEAT	Holger Grotjans	AEA Technology GmbH	CFX-TASCflow
		Germany

CKD	Ales Skotak	CKD Blansko Engineering, a.s.	FLUENT
		Czech Republic

HQ	Maryse Page	IREQ Institute de recherche	CFX-TASCflow
	Anne-Marie Giroux	dHydro-Quebec	FIDAP
		Canada	FINE/Turbo
HTC	Katsumasa Shimmei	Hitachi, Ltd.
	Takanori Ishii
	Kazuo Niikura

NUT	Sadao Kurosawa	Toshiba Corporation, Japan
	Tomotatsu Nagafuji	Nagoya University, Japan
	Debasish Biswas	Toshiba Corporation, Japan

TEV	Per Egil Skåre	Sintef Energy Research, Norway	FLUENT
	Ole Gunnar Dahlhaug	Norwegian University of
		Science and Technology, Norway

VUAB	Staffan Jonzén	Vattenfall Utveckling AB	FLUENT
	Bengt Hemström
	Urban Andersson
Iowa	Yong. G. Lai	Iowa Institute of Hydraulic	U2RANS
	V.C. Patel	Research, U.S.A.

LTU	Michel Cervantes	Luleå University of Technology	CFX-4.3
	Fredrik Engström	Sweden

EXA	Alain Bélanger	Exa Corporation, U.S.A.	PowerFlow

Experiment	Urban Andersson	Vattenfall Utveckling AB

Table 3.2 contains a summary description of all test cases.

Table 3.3 is a description of all available data files which the computors were asked to provide from their computations. The data from VUAB:s computation are chosen to illustrate typical computational results for the case T(r ).

NAME	GNDPs			PDPs (problem definition parameters)			MPs (measured parameters)
	N₁₁ (√m/60s)	Q₁₁ (√m/s)	Re_H (10^-6)	Head (m)	Flow rate (m³/s)	Runner speed (rpm)	detailed data	DOAPs
CFD 1a (T(r)-case)	140.4	0.98	4.1	4.5	0.516	595	C_p, U, V, k	Cp_{r wall}, Cp_{r average}ζ, α, β, S
CFD 2a (R(r)-case)	140.4	1.02 / 1.05	4.1	4.5	0.542 / 0.554	595	C_p, U,V, k	Cp_{r wall}, Cp_{r average}ζ, &alpha, β, S

Table 3.2. Summary description of all test cases

	Section Ia		Section Ib	Section II	Section III
	U V W C_p	k ε	U V W C_p	U V W C_p	U V W C_p	k ε
CFD 1a	TrIa_VelCp_CFD.dat	TrIa_keps_CFD.dat	TrIb_CFD.dat	TrII_CFD.dat	TrIII_CFD.dat	TrIII_keps_CFD.dat
CFD 2a	RrIa_VelCp_CFD.dat	RrIa_keps_CFD.dat	RrIb_CFD.dat	RrII_CFD.dat	RrIII_CFD.dat	RrIII_keps_CFD.dat
	Section Ia W	Section IVa	Section IVb	Upper centre line	Lower centre line	DOAPs, or other miscellaneous data
	C_p	U V W C_p	U V W C_p	Cp Cf	Cp Cf
CFD 1a	TrIaW_CFD.dat	TrIVa_CFD.dat	TrIVb_CFD.dat Wall pressure: TrIVbW_CFD.dat	TrUcl_Cp_CFD.dat TrUcl_Cf_CFD.dat	TrLcl_Cp_CFD.dat TrLcl_Cf_CFD.dat	TrDOAP_CFD.dat
CFD 2a	RrIaW_CFD.dat	RrIVa_CFD.dat	RrIVb_CFD.dat Wall pressure: TrIVbW_CFD.dat	RrUcl_Cp_CFD.dat RrUcl_Cf_CFD.dat	RrLcl_Cp_CFD.dat RrLcl_Cf_CFD.dat	RrDOAP_CFD.dat

Table 3.3. Description of all available data files, and simulated parameters.

Simulation Case

Solution strategy

The different workshop participants used different codes, both commercial and in-house codes, based on either FVM and FEM, as shown in Table 3.1 where some basic information is available. It was also planned that each group should fill in a Table like Table 3.4. This was however not possible. As an example, however, we show Table 3.4 filled in by ourselves (VUAB), since VUAB:s results for test case T has been chosen as representing typical results.

All relevant settings for the group can be seen in Table 3.4.

Table 3.4. Solution strategy chosen by VUAB, test case T.

Solution acronym	VUAB
Test case	T
Operating condition
CFD code (version)	Fluent 6.0.20
Authors	Jonzén S., Hemström B. & Andersson U.
Affiliations	Vattenfall Utveckling AB.
Report date	June 2001, later revised

References	Jonzén S., Hemström B. & Andersson U: Turbine 99 Accuracy in CFD Simulations on Draft Tube Flow,paper in Proc.T99W2.

Computational topics	Description	Parameter
Discretization method
Governing equations	Continuity, momentum, turbulent kinetic energy, turbulent dissipation.
Turbulence modelling	Standard k-epsilon
Near-wall treatment	Standard wall functions	K=0.42, E=9.793
Discretization scheme	QUICK. Second order upwind for pressure
Mesh	Modification of first grid by Lai, 707760 cells
Fluid properties	ρ=1000 kg/m3, μ=1006*10-3 Ns/m2
Inlet boundary conditions	Velocities, k and ε are specified
Outlet boundary conditions	Static pressure=0
Convergence criteria	Stable residuals and monitor value of velocity.

Although not provided in the same format here or in ProcT99W2, the corresponding information for the other computations according to the table of acronyms can be extracted from the separate papers included in Proc.T99W2.

Computational Domain

To reduce the variation in results from the first workshop, a common grid was supplied to the workshop participants. The grid is available at http://www.sirius.luth.se/strl/Turbine-99/index.htm.

Due to geometrical problems at the first part of the grid and a rather bad grid quality at the elbow, one conclusion from the second workshop was that an improved grid was needed. Some authors modified in various ways the given grid or used their own grid.

Boundary Conditions

A full summary of experimental data needed to set up a CFD-problem can be found in http://www.sirius.luth.se/strl/Turbine-99/index.htm. The file contains information on the two main velocity components at the inlet, information on the wall roughness, wall pressures at the outlet and suggested assumptions for the third (radial) velocity component at the inlet that can be used to verify CFD-calculations against other simulations.

Both workshops used experimental data from (r) data set and for verification of the quality of a code it is recommended that these data is used with the specifications of Case 1 (T) of the second workshop since this offers the best opportunity for comparisons with other computations. However, for the future validation of the codes the calculations should be focused on the (n) data set since this offers the most consistent data set with a ‘complete’ set of velocity measurements from section I to section III. In the next chapter some additional requirements to obtain simulations with a good agreement with the experiments will be discussed.

Application of Physical Models

Most groups used wall functions.

For the second workshop a constant turbulent length scale at the inlet was suggested. Several workshop participants pointed out that this was not the best possible estimate. A better estimate would be a smaller length than recommended by the organisers.

Numerical Accuracy

Bergström (2000) made a thorough study of the numerical accuracy. The grid error was < 7 % and the iterative error was less than 0.8 %, however, a new grid caused an increase in e.g. Cp of 20%. This shows that the grid topology is very important and that ordinary refinement strategies might not be enough to reveal the total grid error.

The variation in the results between the participants serves as a measurement of the total accuracy comparing different CFD-codes and discretisation schemes. For Case T(r) most participants used the recommended grid, which facilitates comparisons between different computed results.

Comparing different computations revealed that the evaluation of the DOAPs was extremely sensitive to the evaluation algorithm. Therefore, these parameters were recomputed by the organisers to reduce the error and to give a constant numerical error. Details are given in Engström et al (2003).

CFD Results

Grid:

Workshop 2-grid

New grid

Derived data for comparison:

ASCII-files with DOAPs for the different cases submitted to the workshop for comparisons.

DOAPs calculated at available cross sections for case T(r). Both workshop 1 and 2.

TrDOAP_CFD.dat

DOAPs calculated at available cross sections for case R(r). Workshop 2.

RrDOAP_CFD.dat

Case T

Velocity and pressure values:

Section Ia

Computed velocity components and normalised pressure (Cp)
at cross section Ia, for Case T(r). (See Figure 1.5).

TrIa_VelCp_CFD.dat

Computed turbulent kinetic energy and turbulent dissipation rate
at cross section Ia, for Case T(r). (See Figure 1.5).

TrIa_keps_CFD.dat

Computed normalised wall pressure (Cp) at cross section Ia, for Case T(r).
(See Figure 1.5).

TrIaW_CFD.dat

Section Ib

Computed velocity components and pressure normalised pressure (Cp) at cross section Ib,
for Case T(r). (See Figure 1.5).

TrIb_CFD.dat

Section II

Computed velocity components and normalised pressure (Cp) at cross section II
for Case T(r). (See Figure 1.4).

TrII_CFD.dat

Section III

Computed velocity components and normalised pressure (Cp) at cross section III,
for Case T(r). (See Figure 1.4).

TrIII_CFD.dat

Computed turbulent kinetic energy and turbulent dissipation rate at cross section III,
for Case T(r). (See Figure 1.5).

TrIII_keps_CFD.dat

Section IVa

Computed velocity components and normalised pressure (Cp) at cross section IVa,
for Case T(r). (See Figure 1.4).

TrIVa_CFD.dat

Section IVb

Computed velocity components and normalised pressure (Cp) at cross section IVb,
for Case T(r). (See Figure 1.4).

TrIVb_CFD.dat

Computed normalised wall pressure (Cp) at cross section IVb, for Case T(r).
(See Figure 1.4).

TrIVbW_CFD.dat

Centrelines

Computed normalised wall pressure along the upper centre line, for Case T(r).
(See Figure 1.7).

TrUcl_Cp_CFD.dat

Computed normalised wall pressure along the lower centre line, for Case T(r).
(See Figure 1.7).

TrLcl_Cp_CFD.dat

Computed normalised wall shear stress (Cf) along the upper centre line,
for Case T(r). (See Figure 1.7).

TrUcl_Cf_CFD.dat

Computed normalised wall shear stress (Cf) along the lower centre line,
for Case T(r). (See Figure 1.7).

TrLcl_Cf_CFD.dat

Case R

Velocity and pressure values:

Section Ia

Computed velocity components and normalised pressure (Cp)
at cross section Ia for Case R(r). (See Figure 1.5).

RrIa_VelCp_CFD.dat

Computed turbulent kinetic energy and turbulent dissipation rate
at cross section Ia, for Case R(r). (See Figure 1.5).

RrIa_keps_CFD.dat

Computed normalised wall pressure (Cp) at cross section Ia, for Case R(r).
(See Figure 1.5).

RrIaW_CFD.dat

Section Ib

Computed velocity components and pressure normalised pressure (Cp)
at cross section Ib, for Case R(r). (See Figure 1.5).

RrIb_CFD.dat

Section II

Computed velocity components and normalised pressure (Cp)
at cross section II for Case R(r). (See Figure 1.4).

RrII_CFD.dat

Section III

Computed velocity components and normalised pressure (Cp)
at cross section III, for Case R(r). (See Figure 1.4).

RrIII_CFD.dat

Computed turbulent kinetic energy and turbulent dissipation rate
at cross section III, for Case R(r). (See Figure 1.5).

RrIII_keps_CFD.dat

Section IVa

Computed velocity components and normalised pressure (Cp)
at cross section IVa, for Case R(r). (See Figure 1.4).

RrIVa_CFD.dat

Section IVb

Computed velocity components and normalised pressure (Cp)
at cross section IVb, for Case R(r). (See Figure 1.4).

RrIVb_CFD.dat

Computed normalised wall pressure (Cp) at cross section IVb, for Case R(r).
(See Figure 1.4).

RrIVbW_CFD.dat

Centrelines

Computed normalised wall pressure along the upper centre line, for Case R(r).
(See Figure 1.7).

RrUcl_Cp_CFD.dat

Computed normalised wall pressure along the lower centre line, for Case R(r).
(See Figure 1.7).

RrLcl_Cp_CFD.dat

Computed normalised wall shear stress (Cf) along the upper centre line, for Case R(r).
(See Figure 1.7).

RrUcl_Cf_CFD.dat

Computed normalised wall shear stress (Cf) along the lower centre line,
for Case R(r). (See Figure 1.7).

RrLcl_Cf_CFD.dat

References

Bergström, J. (2000). “Modeling and Numerical Simulation of Hydro Power Flows”. Doctoral Thesis 2000-06, Luleå University of Technology, Department of Mechanical Engineering, Division of Fluid Mechanics.

Casey M. & Wintergerste T. (editors). (2000) ERCOFTAC Best Practice Guidelines. ERCOFTAC Special Interest Group on “Quality and Trust in Industrial CFD”.

Gebart B.R., Gustavsson L.H. & Karlsson R.I. (editors) (2000a) "Turbine 99 – Workshop on Draft Tube Flow”. Technical Report 2000-11, Luleå University of Technology, Department of Mechanical Engineering, Division of Fluid Mechanics.

Gebart B.R., Gustavsson L.H. & Karlsson R.I. (2000b) "Report from Turbine 99 – Workshop on Draft Tube Flow in Porjus, Sweden, 20-23 June 1999”. Paper presented at the 20^th IAHR Symposium Hydraulic Machinery and Systems. Aug. 6-9, 2000, Charlotte, North Carolina, U.S.A.

Engström T.F., Gustavsson L.H. & Karlsson R.I. (2002) "Report from Turbine 99 – Workshop 2 on Draft Tube Flow”. The second ERCOFTAC Workshop on Draft Tube Flow, held in Älvkarleby, Sweden, June 18-20, 2001. Paper presented at the 21^st IAHR Symposium Hydraulic Machinery and Systems, Lausanne, Switzerland, Sept. 2002

Engström, T.F., Gustavsson, L.H., & Karlsson, R.I. (2003), Proceedings of Turbine-99 - Workshop 2. The second ERCOFTAC Workshop on Draft Tube Flow. Älvkarleby, Sweden, June 18-20 2001. Available on the web, http://www.sirius.luth.se/strl/Turbine-99/index.htm (bad link, DCE 10-03-10)

In text called Proc.W2.

Contributors: Rolf Karlsson - Vattenfall Utveckling AB