Hybrid hydrodynamic model

Dear all

I am currently using the hybrid hydrodynamic model to investigate the modification of Ca and Cd, taking into account the wave excitation force, radiation damping, and hydrostatic based on potential theory, while also considering the added mass and drag force terms in the strip theory. I’ve set the added mass at 0 frequency in the .1 file to 0 and set the PropPot property of the Morison element to FALSE.

However, when using this model to simulate surge free decay, I noticed that the equilibrium position of the time-domain motion curve is not near zero (which it is when only potential theory is adopted). This has led me to suspect that there might be some additional forces that I have overlooked.

The settings in mooring ,ElastoDyn.dat and HydroDyn.dat are same for both models except for the Morison elements/joints and PtfmVol0( 0 for Hybrid model). I will attach the HydroDyn and ElastoDyn settings for the hybrid model below

------- HydroDyn v2.03.* Input File --------------------------------------------
Generated with AeroElasticSE FAST driver
False                  Echo        - Echo the input file data (flag)
---------------------- ENVIRONMENTAL CONDITIONS --------------------------------
1025.0                 WtrDens     - Water density (kg/m^3)
2.5                 WtrDpth     - Water depth (meters)
0.0                    MSL2SWL     - Offset between still-water level and mean sea level (meters) [positive upward; unused when WaveMod = 6; must be zero if PotMod=1 or 2]
---------------------- WAVES ---------------------------------------------------
0                      WaveMod     - Incident wave kinematics model {0: none=still water, 1: regular (periodic), 1P#: regular with user-specified phase, 2: JONSWAP/Pierson-Moskowitz spectrum (irregular), 3: White noise spectrum (irregular), 4: user-defined spectrum from routine UserWaveSpctrm (irregular), 5: Externally generated wave-elevation time series, 6: Externally generated full wave-kinematics time series [option 6 is invalid for PotMod/=0]} (switch)
0                      WaveStMod   - Model for stretching incident wave kinematics to instantaneous free surface {0: none=no stretching, 1: vertical stretching, 2: extrapolation stretching, 3: Wheeler stretching} (switch) [unused when WaveMod=0 or when PotMod/=0]
1200                   WaveTMax    - Analysis time for incident wave calculations (sec) [unused when WaveMod=0; determines WaveDOmega=2Pi/WaveTMax in the IFFT]
0.25                   WaveDT      - Time step for incident wave calculations     (sec) [unused when WaveMod=0; 0.1<=WaveDT<=1.0 recommended; determines WaveOmegaMax=Pi/WaveDT in the IFFT]
0.02                   WaveHs      - Significant wave height of incident waves (meters) [used only when WaveMod=1, 2, or 3]
1.01 WaveTp         - Significant wave height of incident waves (meters) [used only when WaveMod=1, 2, or 3]
Default                WavePkShp   - Peak-shape parameter of incident wave spectrum (-) or DEFAULT (string) [used only when WaveMod=2; use 1.0 for Pierson-Moskowitz]
0.031415926535         WvLowCOff   - Low  cut-off frequency or lower frequency limit of the wave spectrum beyond which the wave spectrum is zeroed (rad/s) [unused when WaveMod=0, 1, or 6]
3.141592653589         WvHiCOff    - High cut-off frequency or upper frequency limit of the wave spectrum beyond which the wave spectrum is zeroed (rad/s) [unused when WaveMod=0, 1, or 6]
0.0                    WaveDir     - Incident wave propagation heading direction                         (degrees) [unused when WaveMod=0 or 6]
0                      WaveDirMod  - Directional spreading function {0: none, 1: COS2S}                  (-)       [only used when WaveMod=2,3, or 4]
1.0                    WaveDirSpread - Wave direction spreading coefficient ( > 0 )                        (-)       [only used when WaveMod=2,3, or 4 and WaveDirMod=1]
1                      WaveNDir    - Number of wave directions                                           (-)       [only used when WaveMod=2,3, or 4 and WaveDirMod=1; odd number only]
1.5707963267948966     WaveDirRange - Range of wave directions (full range: WaveDir +/- 1/2*WaveDirRange) (degrees) [only used when WaveMod=2,3,or 4 and WaveDirMod=1]
304524126              WaveSeed(1) - First  random seed of incident waves [-2147483648 to 2147483647]    (-)       [unused when WaveMod=0, 5, or 6]
RANLUX                 WaveSeed(2) - Second random seed of incident waves [-2147483648 to 2147483647]    (-)       [unused when WaveMod=0, 5, or 6] for intrinsic pRNG, or an alternative pRNG: "RanLux"
True                   WaveNDAmp   - Flag for normally distributed amplitudes                            (flag)    [only used when WaveMod=2, 3, or 4]
""                     WvKinFile   - Root name of externally generated wave data file(s)        (quoted string)    [used only when WaveMod=5 or 6]
1                      NWaveElev   - Number of points where the incident wave elevations can be computed (-)       [maximum of 9 output locations]
0.0                    WaveElevxi  - List of xi-coordinates for points where the incident wave elevations can be output (meters) [NWaveElev points, separated by commas or white space; usused if NWaveElev = 0]
0.0                    WaveElevyi  - List of yi-coordinates for points where the incident wave elevations can be output (meters) [NWaveElev points, separated by commas or white space; usused if NWaveElev = 0]
---------------------- 2ND-ORDER WAVES ----------------------------------------- [unused with WaveMod=0 or 6]
False                  WvDiffQTF   - Full difference-frequency 2nd-order wave kinematics (flag)
False                  WvSumQTF    - Full summation-frequency  2nd-order wave kinematics (flag)
0.0                    WvLowCOffD  - Low  frequency cutoff used in the difference-frequencies (rad/s) [Only used with a difference-frequency method]
0.737863               WvHiCOffD   - High frequency cutoff used in the difference-frequencies (rad/s) [Only used with a difference-frequency method]
0.314159               WvLowCOffS  - Low  frequency cutoff used in the summation-frequencies  (rad/s) [Only used with a summation-frequency  method]
3.2                    WvHiCOffS   - High frequency cutoff used in the summation-frequencies  (rad/s) [Only used with a summation-frequency  method]
---------------------- CURRENT ------------------------------------------------- [unused with WaveMod=6]
0                      CurrMod     - Current profile model {0: none=no current, 1: standard, 2: user-defined from routine UserCurrent} (switch)
0.0                    CurrSSV0    - Sub-surface current velocity at still water level  (m/s) [used only when CurrMod=1]
0.0                    CurrSSDir   - Sub-surface current heading direction (degrees) or DEFAULT (string) [used only when CurrMod=1]
20.0                   CurrNSRef   - Near-surface current reference depth            (meters) [used only when CurrMod=1]
0.0                    CurrNSV0    - Near-surface current velocity at still water level (m/s) [used only when CurrMod=1]
0.0                    CurrNSDir   - Near-surface current heading direction         (degrees) [used only when CurrMod=1]
0.0                    CurrDIV     - Depth-independent current velocity                 (m/s) [used only when CurrMod=1]
0.0                    CurrDIDir   - Depth-independent current heading direction    (degrees) [used only when CurrMod=1]
---------------------- FLOATING PLATFORM --------------------------------------- [unused with WaveMod=6]
1                      PotMod      - Potential-flow model {0: none=no potential flow, 1: frequency-to-time-domain transforms based on WAMIT output, 2: fluid-impulse theory (FIT)} (switch)
1                      ExctnMod    - Wave Excitation model {0: None, 1: DFT, 2: state-space} (switch) [only used when PotMod=1; STATE-SPACE REQUIRES *.ssexctn INPUT FILE]
1                      RdtnMod     - Radiation memory-effect model {0: no memory-effect calculation, 1: convolution, 2: state-space} (switch) [only used when PotMod=1; STATE-SPACE REQUIRES *.ss INPUT FILE]
60.0                   RdtnTMax    - Analysis time for wave radiation kernel calculations (sec) [only used when PotMod=1; determines RdtnDOmega=Pi/RdtnTMax in the cosine transform; MAKE SURE THIS IS LONG ENOUGH FOR THE RADIATION IMPULSE RESPONSE FUNCTIONS TO DECAY TO NEAR-ZERO FOR THE GIVEN PLATFORM!]
DEFAULT                RdtnDT      - Time step for wave radiation kernel calculations (sec) [only used when PotMod=1; DT<=RdtnDT<=0.1 recommended; determines RdtnOmegaMax=Pi/RdtnDT in the cosine transform]
1                      NBody       - Number of WAMIT bodies to be used (-) [>=1; only used when PotMod=1. If NBodyMod=1, the WAMIT data contains a vector of size 6*NBody x 1 and matrices of size 6*NBody x 6*NBody; if NBodyMod>1, there are NBody sets of WAMIT data each with a vector of size 6 x 1 and matrices of size 6 x 6]
1                      NBodyMod    - Body coupling model {1: include coupling terms between each body and NBody in HydroDyn equals NBODY in WAMIT, 2: neglect coupling terms between each body and NBODY=1 with XBODY=0 in WAMIT, 3: Neglect coupling terms between each body and NBODY=1 with XBODY=/0 in WAMIT} (switch) [only used when PotMod=1]
"HydroData/1-50"               PotFile     - Root name of potential-flow model data; WAMIT output files containing the linear, nondimensionalized, hydrostatic restoring matrix (.hst), frequency-dependent hydrodynamic added mass matrix and damping matrix (.1), and frequency- and direction-dependent wave excitation force vector per unit wave amplitude (.3) (quoted string) [MAKE SURE THE FREQUENCIES INHERENT IN THESE WAMIT FILES SPAN THE PHYSICALLY-SIGNIFICANT RANGE OF FREQUENCIES FOR THE GIVEN PLATFORM; THEY MUST CONTAIN THE ZERO- AND INFINITE-FREQUENCY LIMITS!]
1.0                    WAMITULEN   - Characteristic body length scale used to redimensionalize WAMIT output (meters) [only used when PotMod=1]
0                      PtfmRefxt   - The xt offset of the body reference point(s) from (0,0,0) (meters) [1 to NBody] [only used when PotMod=1]
0                      PtfmRefyt   - The yt offset of the body reference point(s) from (0,0,0) (meters) [1 to NBody] [only used when PotMod=1]
0                      PtfmRefzt   - The zt offset of the body reference point(s) from (0,0,0) (meters) [1 to NBody] [only used when PotMod=1. If NBodyMod=2,PtfmRefzt=0.0]
0                      PtfmRefztRot - The rotation about zt of the body reference frame(s) from xt/yt (degrees) [1 to NBody] [only used when PotMod=1]
0                      PtfmVol0    - Displaced volume of water when the platform is in its undisplaced position (m^3) [only used when PotMod=1; USE THE SAME VALUE COMPUTED BY WAMIT AS OUTPUT IN THE .OUT FILE!]
0.0                    PtfmCOBxt   - The xt offset of the center of buoyancy (COB) from the platform reference point (meters)  [only used when PotMod=1]
0.0                    PtfmCOByt   - The yt offset of the center of buoyancy (COB) from the platform reference point (meters)  [only used when PotMod=1]
---------------------- 2ND-ORDER FLOATING PLATFORM FORCES ---------------------- [unused with WaveMod=0 or 6, or PotMod=0 or 2]
0                      MnDrift     - Mean-drift 2nd-order forces computed                                       {0: None; [7, 8, 9, 10, 11, or 12]: WAMIT file to use} [Only one of MnDrift, NewmanApp, or DiffQTF can be non-zero]
0                      NewmanApp   - Mean- and slow-drift 2nd-order forces computed with Newman's approximation {0: None; [7, 8, 9, 10, 11, or 12]: WAMIT file to use} [Only one of MnDrift, NewmanApp, or DiffQTF can be non-zero. Used only when WaveDirMod=0]
0                      DiffQTF     - Full difference-frequency 2nd-order forces computed with full QTF          {0: None; [10, 11, or 12]: WAMIT file to use}          [Only one of MnDrift, NewmanApp, or DiffQTF can be non-zero]
0                      SumQTF      - Full summation -frequency 2nd-order forces computed with full QTF          {0: None; [10, 11, or 12]: WAMIT file to use}
---------------------- PLATFORM ADDITIONAL STIFFNESS AND DAMPING  --------------
0.0              AddF0    - Additional preload (N, N-m) [If NBodyMod=1, one size 6*NBody x 1 vector; if NBodyMod>1, NBody size 6 x 1 vectors]
0.0              
0.0              
0.0              
0.0              
0.0              
0.0            0.0            0.0            0.0            0.0            0.0   AddCLin  - Additional linear stiffness (N/m, N/rad, N-m/m, N-m/rad)
0.0            0.0            0.0            0.0            0.0            0.0
0.0            0.0            0.0            0.0            0.0            0.0
0.0            0.0            0.0            0              0.0            0.0
0.0            0.0            0.0            0.0            0              0.0
0.0            0.0            0.0            0.0            0.0            0.0
0.0            0.0            0.0            0.0            0.0            0.0   AddBLin  - Additional linear damping(N/(m/s), N/(rad/s), N-m/(m/s), N-m/(rad/s))
0.0            0.0            0.0            0.0            0.0            0.0
0.0            0.0            0.0            0.0            0.0            0.0
0.0            0.0            0.0            0.0            0.0            0.0
0.0            0.0            0.0            0.0            0.0            0.0
0.0            0.0            0.0            0.0            0.0            0.0
0.0            0.0            0.0            0.0            0.0            0.0   AddBQuad - Additional quadratic drag(N/(m/s)^2, N/(rad/s)^2, N-m(m/s)^2, N-m/(rad/s)^2)
0.0            0.0            0.0            0.0            0.0            0.0
0.0            0.0            0.0            0.0            0.0            0.0
0.0            0.0            0.0            0.0            0.0            0.0
0.0            0.0            0.0            0.0            0.0            0.0
0.0            0.0            0.0            0.0            0.0            0.0
---------------------- AXIAL COEFFICIENTS --------------------------------------
3                      NAxCoef     - Number of axial coefficients (-)
AxCoefID      AxCd        AxCa        AxCp    
(-)         (-)         (-)         (-)    
1     0.00     0.00     1.00
2     0.95     0        1
3     0.95     0        1
---------------------- MEMBER JOINTS -------------------------------------------
24                    NJoints     - Number of joints (-)   [must be exactly 0 or at least 2]
JointID     Jointxi     Jointyi     Jointzi    JointAxID  JointOvrlp   ! [JointOvrlp= 0: do nothing at joint, 1: eliminate overlaps by calculating super member]
(-)         (m)         (m)         (m)         (-)      (switch)  
1	-0.58	0	-0.3	2	0
2	-0.58	0	0.06	1	0
3	0.29	0.5023	-0.3	2	0
4	0.29	0.5023	0.06	1	0
5	0.29	-0.5023	-0.3	2	0
6	0.29	-0.5023	0.06	1	0
7	0	0	-0.3	3	0
8	0	0	0.12	1	0
9	-0.58	0	-0.38	1	0
10	0.29	0.5023	-0.38	1	0
11	0.29	-0.5023	-0.38	1	0
12	0	0	-0.38	1	0
13	-0.443	0	-0.34	1	0
14	-0.113	0	-0.34	1	0
15	0.2216	0.38365	-0.34	1	0
16	0.3866	0.669438383	-0.34	1	0
17	0.2216	-0.38365	-0.34	1	0
18	0.3866	-0.669438383	-0.34	1	0
19	-0.274	0	0.1	1	0
20	-0.531409215	0	-0.210429677	1	0
21	0.137	0.2373	0.1	1	0
22	0.261982521	0.460413318	-0.210429677	1	0
23	0.137	-0.2373	0.1	1	0
24	0.261982521	-0.460413318	-0.210429677	1	0   
---------------------- MEMBER CROSS-SECTION PROPERTIES -------------------------
6          NPropSets   - Number of member property sets (-)
PropSetID     PropD     PropThck  
(-)         (m)         (m)    
1	0.136	0.015
2	0.1	    0.015
3	0.28	0.015
4	0.218	0.015
5	0.08	0.015
6	0.045	0.015   
---------------------- SIMPLE HYDRODYNAMIC COEFFICIENTS (model 1) --------------
SimplCd    SimplCdMG    SimplCa    SimplCaMG    SimplCp    SimplCpMG   SimplAxCd  SimplAxCdMG  SimplAxCa  SimplAxCaMG  SimplAxCp  SimplAxCpMG
(-)         (-)         (-)         (-)         (-)         (-)         (-)         (-)         (-)         (-)         (-)         (-)    
0.6         0.6         1.0         1.0         1.0         1.0         0.0         0.0         0.0         0.0         0.0         0.0    
---------------------- DEPTH-BASED HYDRODYNAMIC COEFFICIENTS (model 2) ---------
0           NCoefDpth   - Number of depth-dependent coefficients (-)
Dpth       DpthCd     DpthCdMG     DpthCa     DpthCaMG     DpthCp     DpthCpMG    DpthAxCd   DpthAxCdMG   DpthAxCa   DpthAxCaMG   DpthAxCp   DpthAxCpMG 
(m)         (-)         (-)         (-)         (-)         (-)         (-)         (-)         (-)         (-)         (-)         (-)         (-)    
---------------------- MEMBER-BASED HYDRODYNAMIC COEFFICIENTS (model 3) --------
14           NCoefMembers - Number of member-based coefficients (-)
MemberID_HydC  MemberCd1   MemberCd2  MemberCdMG1 MemberCdMG2  MemberCa1   MemberCa2  MemberCaMG1 MemberCaMG2  MemberCp1   MemberCp2  MemberCpMG1 MemberCpMG2 MemberAxCd1 MemberAxCd2 MemberAxCdMG1 MemberAxCdMG2 MemberAxCa1 MemberAxCa2 MemberAxCaMG1 MemberAxCaMG2 MemberAxCp1 MemberAxCp2 MemberAxCpMG1 MemberAxCpMG2
(-)         (-)         (-)         (-)         (-)         (-)         (-)         (-)         (-)         (-)         (-)         (-)         (-)         (-)         (-)         (-)         (-)         (-)         (-)         (-)         (-)         (-)         (-)         (-)         (-)    
1  0.6 0.6 0 0 0.7 0.7   0	0	0	0	0	0	0	0	0	0	0	0	0	0 0	0 0	0
2  0.6 0.6 0 0 0.7 0.7	 0	0	0	0	0	0	0	0	0	0	0	0	0	0 0 0 0 0
3  0.6 0.6 0 0 0.7 0.7	 0	0	0	0	0	0	0	0	0	0	0	0	0	0 0 0 0 0
4  0.6 0.6 0 0 0.7 0.7   0	0	0	0	0	0	0	0	0	0	0	0	0	0 0	0 0	0
5  0.6 0.6 0 0 0.7 0.7   0	0	0	0	0	0	0	0	0	0	0	0	0	0 0	0 0	0
6  0.6 0.6 0 0 0.7 0.7   0	0	0	0	0	0	0	0	0	0	0	0	0	0 0	0 0	0
7  0.6 0.6 0 0 0.7 0.7   0	0	0	0	0	0	0	0	0	0	0	0	0	0 0	0 0	0
8  0.6 0.6 0 0 0.7 0.7   0	0	0	0	0	0	0	0	0	0	0	0	0	0 0	0 0	0
9  0.6 0.6 0 0 0.7 0.7   0	0	0	0	0	0	0	0	0	0	0	0	0	0 0	0 0	0
10 0.6 0.6 0 0 0.7 0.7   0	0	0	0	0	0	0	0	0	0	0	0	0	0 0	0 0	0
11 0.6 0.6 0 0 0.7 0.7   0	0	0	0	0	0	0	0	0	0	0	0	0	0 0	0 0	0
12 0.6 0.6 0 0 0.7 0.7   0	0	0	0	0	0	0	0	0	0	0	0	0	0 0	0 0	0
13 0.6 0.6 0 0 0.7 0.7   0	0	0	0	0	0	0	0	0	0	0	0	0	0 0	0 0	0
14 0.6 0.6 0 0 0.7 0.7   0	0	0	0	0	0	0	0	0	0	0	0	0	0 0	0 0	0
-------------------- MEMBERS -------------------------------------------------
14          NMembers    - Number of members (-)
MemberID    MJointID1   MJointID2  MPropSetID1 MPropSetID2  MDivSize    MCoefMod     PropPot   !  [MCoefMod=1: use simple coeff table, 2: use depth-based coeff table, 3: use member-based coeff table] [ PropPot/=0 if member is modeled with potential-flow theory]
(-)         (-)         (-)         (-)         (-)         (m)      (switch)     (flag)   
1	2	1	1	1	0.2	3	FALSE
2	3	4	1	1	0.2	3	FALSE
3	5	6	1	1	0.2	3	FALSE
4	7	8	2	2	0.2	3	FALSE
5	9	1	3	3	0.2	3	FALSE
6	10	3	3	3	0.2	3	FALSE
7	11	5	3	3	0.2	3	FALSE
8	12	7	4	4	0.2	3	FALSE
9	13	14	5	5	0.2	3	FALSE
10	15	16	5	5	0.2	3	FALSE
11	17	18	5	5	0.2	3	FALSE
12	19	20	6	6	0.2	3	FALSE
13	21	22	6	6	0.2	3	FALSE
14	23	24	6	6	0.2	3	FALSE
---------------------- FILLED MEMBERS ------------------------------------------
0           NFillGroups - Number of filled member groups (-) [If FillDens = DEFAULT, then FillDens = WtrDens; FillFSLoc is related to MSL2SWL]
FillNumM    FillMList   FillFSLoc   FillDens  
(-)         (-)         (m)      (kg/m^3) 
---------------------- MARINE GROWTH -------------------------------------------
0           NMGDepths   - Number of marine-growth depths specified (-)
MGDpth      MGThck      MGDens   
(m)         (m)      (kg/m^3)  
---------------------- DEGREES OF FREEDOM --------------------------------------
False                 FlapDOF1    - First flapwise blade mode DOF (flag)
False                 FlapDOF2    - Second flapwise blade mode DOF (flag)
False                 EdgeDOF     - First edgewise blade mode DOF (flag)
False                 TeetDOF     - Rotor-teeter DOF (flag) [unused for 3 blades]
False                 DrTrDOF     - Drivetrain rotational-flexibility DOF (flag)
False                 GenDOF      - Generator DOF (flag)
False                 YawDOF      - Yaw DOF (flag)
False                 TwFADOF1    - First fore-aft tower bending-mode DOF (flag)
False                 TwFADOF2    - Second fore-aft tower bending-mode DOF (flag)
False                 TwSSDOF1    - First side-to-side tower bending-mode DOF (flag)
False                 TwSSDOF2    - Second side-to-side tower bending-mode DOF (flag)
True                   PtfmSgDOF   - Platform horizontal surge translation DOF (flag)
True                   PtfmSwDOF   - Platform horizontal sway translation DOF (flag)
True                   PtfmHvDOF   - Platform vertical heave translation DOF (flag)
True                   PtfmRDOF    - Platform roll tilt rotation DOF (flag)
True                   PtfmPDOF    - Platform pitch tilt rotation DOF (flag)
True                   PtfmYDOF    - Platform yaw rotation DOF (flag)
---------------------- INITIAL CONDITIONS --------------------------------------
0.0                    OoPDefl     - Initial out-of-plane blade-tip displacement (meters)
0.0                    IPDefl      - Initial in-plane blade-tip deflection (meters)
0.0                    BlPitch(1)  - Blade 1 initial pitch (degrees)
0.0                    BlPitch(2)  - Blade 2 initial pitch (degrees)
0.0                    BlPitch(3)  - Blade 3 initial pitch (degrees) [unused for 2 blades]
0.0                    TeetDefl    - Initial or fixed teeter angle (degrees) [unused for 3 blades]
0.0                    Azimuth     - Initial azimuth angle for blade 1 (degrees)
0                   RotSpeed    - Initial or fixed rotor speed (rpm)
0.0                    NacYaw      - Initial or fixed nacelle-yaw angle (degrees)
0.0                    TTDspFA     - Initial fore-aft tower-top displacement (meters)
0.0                    TTDspSS     - Initial side-to-side tower-top displacement (meters)
0.01                    PtfmSurge   - Initial or fixed horizontal surge translational displacement of platform (meters)
0.0                    PtfmSway    - Initial or fixed horizontal sway translational displacement of platform (meters)
0.0                    PtfmHeave   - Initial or fixed vertical heave translational displacement of platform (meters)
0.0                    PtfmRoll    - Initial or fixed roll tilt rotational displacement of platform (degrees)
0.0                    PtfmPitch   - Initial or fixed pitch tilt rotational displacement of platform (degrees)
0.0                    PtfmYaw     - Initial or fixed yaw rotational displacement of platform (degrees)
---------------------- TURBINE CONFIGURATION -----------------------------------

I would greatly appreciate it if someone could point out where the problem lies.

Thanks a lot in advance!

Dear @Teng.Long,

I’m not sure why your hybrid solution is not oscillating about zero. Does it do this if you set all of the drag coefficients (AxCd and MemberCd) to zero?

FYI: Normally I’d expect hybrid potential-flow theory+ strip-theory models to only consider viscous drag in the strip theory solution; in your case, you’ve mixed and matched terms a bit. It is also a bit odd to me that you’d define zero AxCa and nonzero AxCp for the axial coefficients whereas you’ve defined nonzero MemberCa and zero MemberCp for the transverse coefficients.

Best regards,