8.1
general documentation
Data Structures | Enumerations | Functions | Variables
cs_wall_functions.h File Reference
#include "bft_printf.h"
#include "cs_base.h"
#include "cs_math.h"
#include "cs_turbulence_model.h"
+ Include dependency graph for cs_wall_functions.h:

Go to the source code of this file.

Data Structures

struct  cs_wall_functions_t
 wall functions descriptor. More...
 

Enumerations

enum  cs_wall_f_type_t {
  CS_WALL_F_UNSET = -999 , CS_WALL_F_DISABLED = 0 , CS_WALL_F_1SCALE_POWER = 1 , CS_WALL_F_1SCALE_LOG = 2 ,
  CS_WALL_F_2SCALES_LOG = 3 , CS_WALL_F_SCALABLE_2SCALES_LOG = 4 , CS_WALL_F_2SCALES_VDRIEST = 5 , CS_WALL_F_2SCALES_SMOOTH_ROUGH = 6 ,
  CS_WALL_F_2SCALES_CONTINUOUS = 7
}
 
enum  cs_wall_f_s_type_t {
  CS_WALL_F_S_UNSET = -999 , CS_WALL_F_S_ARPACI_LARSEN = 0 , CS_WALL_F_S_VDRIEST = 1 , CS_WALL_F_S_LOUIS = 2 ,
  CS_WALL_F_S_MONIN_OBUKHOV = 3 , CS_WALL_F_S_SMOOTH_ROUGH = 4
}
 

Functions

static void cs_wall_functions_1scale_power (cs_real_t l_visc, cs_real_t vel, cs_real_t y, int *iuntur, cs_gnum_t *nsubla, cs_gnum_t *nlogla, cs_real_t *ustar, cs_real_t *uk, cs_real_t *yplus, cs_real_t *ypup, cs_real_t *cofimp)
 Power law: Werner & Wengle. More...
 
static void cs_wall_functions_1scale_log (cs_real_t l_visc, cs_real_t vel, cs_real_t y, int *iuntur, cs_gnum_t *nsubla, cs_gnum_t *nlogla, cs_real_t *ustar, cs_real_t *uk, cs_real_t *yplus, cs_real_t *ypup, cs_real_t *cofimp)
 Log law: piecewise linear and log, with one velocity scale based on the friction. More...
 
static cs_real_t _uplus (cs_real_t yp, cs_real_t ka, cs_real_t B, cs_real_t cuv, cs_real_t y0, cs_real_t n)
 
static cs_real_t _dupdyp (cs_real_t yp, cs_real_t ka, cs_real_t B, cs_real_t cuv, cs_real_t y0, cs_real_t n)
 
static void cs_wall_functions_2scales_continuous (cs_real_t rnnb, cs_real_t l_visc, cs_real_t t_visc, cs_real_t vel, cs_real_t y, cs_real_t kinetic_en, int *iuntur, cs_gnum_t *nsubla, cs_gnum_t *nlogla, cs_real_t *ustar, cs_real_t *uk, cs_real_t *yplus, cs_real_t *ypup, cs_real_t *cofimp)
 Continuous law of the wall between the linear and log law, with two velocity scales based on the friction and the turbulent kinetic energy. Can be used with RANS model either in high Reynolds or in low Reynolds (if the underlying RANS model is compatible). More...
 
static void cs_wall_functions_2scales_log (cs_real_t l_visc, cs_real_t t_visc, cs_real_t vel, cs_real_t y, cs_real_t kinetic_en, int *iuntur, cs_gnum_t *nsubla, cs_gnum_t *nlogla, cs_real_t *ustar, cs_real_t *uk, cs_real_t *yplus, cs_real_t *ypup, cs_real_t *cofimp)
 Log law: piecewise linear and log, with two velocity scales based on the friction and the turbulent kinetic energy. More...
 
static void cs_wall_functions_2scales_scalable (cs_real_t l_visc, cs_real_t t_visc, cs_real_t vel, cs_real_t y, cs_real_t kinetic_en, int *iuntur, cs_gnum_t *nsubla, cs_gnum_t *nlogla, cs_real_t *ustar, cs_real_t *uk, cs_real_t *yplus, cs_real_t *dplus, cs_real_t *ypup, cs_real_t *cofimp)
 Scalable wall function: shift the wall if $ y^+ < y^+_{lim} $. More...
 
static cs_real_t _vdriest_dupdyp_integral (cs_real_t yplus)
 
static void cs_wall_functions_2scales_vdriest (cs_real_t rnnb, cs_real_t l_visc, cs_real_t vel, cs_real_t y, cs_real_t kinetic_en, int *iuntur, cs_gnum_t *nsubla, cs_gnum_t *nlogla, cs_real_t *ustar, cs_real_t *uk, cs_real_t *yplus, cs_real_t *ypup, cs_real_t *cofimp, cs_real_t *lmk, cs_real_t kr, bool wf)
 Two velocity scales wall function using Van Driest mixing length. More...
 
static void cs_wall_functions_2scales_smooth_rough (cs_real_t l_visc, cs_real_t t_visc, cs_real_t vel, cs_real_t y, cs_real_t rough_d, cs_real_t kinetic_en, int *iuntur, cs_gnum_t *nsubla, cs_gnum_t *nlogla, cs_real_t *ustar, cs_real_t *uk, cs_real_t *yplus, cs_real_t *dplus, cs_real_t *ypup, cs_real_t *cofimp)
 Two velocity scales wall function with automatic switch from rough to smooth. More...
 
static void cs_wall_functions_disabled (cs_real_t l_visc, cs_real_t t_visc, cs_real_t vel, cs_real_t y, int *iuntur, cs_gnum_t *nsubla, cs_gnum_t *nlogla, cs_real_t *ustar, cs_real_t *uk, cs_real_t *yplus, cs_real_t *dplus, cs_real_t *ypup, cs_real_t *cofimp)
 No wall function. More...
 
static void cs_wall_functions_s_arpaci_larsen (cs_real_t l_visc, cs_real_t prl, cs_real_t prt, cs_real_t rough_t, cs_real_t uk, cs_real_t yplus, cs_real_t dplus, cs_real_t *htur, cs_real_t *yplim)
 The correction of the exchange coefficient is computed thanks to a similarity model between dynamic viscous sub-layer and themal sub-layer. More...
 
static void cs_wall_functions_s_vdriest (cs_real_t prl, cs_real_t prt, cs_real_t yplus, cs_real_t *htur)
 The correction of the exchange coefficient $ h_{tur} = \sigma \dfrac{y^+}{t^+} $ is computed thanks to a numerical integration of: More...
 
static void cs_wall_functions_s_smooth_rough (cs_real_t l_visc, cs_real_t prl, cs_real_t prt, cs_real_t rough_t, cs_real_t uk, cs_real_t yplus, cs_real_t dplus, cs_real_t *htur)
 Rough Smooth Thermal Wall Function - Prototype. More...
 
void wallfunctions (const int *const iwallf, const cs_lnum_t *const ifac, const cs_real_t *const viscosity, const cs_real_t *const t_visc, const cs_real_t *const vel, const cs_real_t *const y, const cs_real_t *const rough_d, const cs_real_t *const rnnb, const cs_real_t *const kinetic_en, int *iuntur, cs_lnum_t *nsubla, cs_lnum_t *nlogla, cs_real_t *ustar, cs_real_t *uk, cs_real_t *yplus, cs_real_t *ypup, cs_real_t *cofimp, cs_real_t *dplus)
 
void hturbp (const int *const iwalfs, const cs_real_t *const l_visc, const cs_real_t *const prl, const cs_real_t *const prt, const cs_real_t *const rough_t, const cs_real_t *const uk, const cs_real_t *const yplus, const cs_real_t *const dplus, cs_real_t *htur, cs_real_t *yplim)
 
cs_wall_functions_t * cs_get_glob_wall_functions (void)
 
void cs_wall_functions_velocity (cs_wall_f_type_t iwallf, cs_real_t l_visc, cs_real_t t_visc, cs_real_t vel, cs_real_t y, cs_real_t rough_d, cs_real_t rnnb, cs_real_t kinetic_en, int *iuntur, cs_gnum_t *nsubla, cs_gnum_t *nlogla, cs_real_t *ustar, cs_real_t *uk, cs_real_t *yplus, cs_real_t *ypup, cs_real_t *cofimp, cs_real_t *dplus)
 Compute the friction velocity and $y^+$ / $u^+$. More...
 
void cs_wall_functions_scalar (cs_wall_f_s_type_t iwalfs, cs_real_t l_visc, cs_real_t prl, cs_real_t prt, cs_real_t rough_t, cs_real_t uk, cs_real_t yplus, cs_real_t dplus, cs_real_t *htur, cs_real_t *yplim)
 Compute the correction of the exchange coefficient between the fluid and the wall for a turbulent flow. More...
 
void cs_immersed_boundary_wall_functions (int f_id, cs_real_t *st_exp, cs_real_t *st_imp)
 Compute boundary contributions for all immersed boundaries. More...
 

Variables

const cs_wall_functions_t * cs_glob_wall_functions
 

Enumeration Type Documentation

◆ cs_wall_f_s_type_t

enum cs_wall_f_s_type_t
Enumerator
CS_WALL_F_S_UNSET 
CS_WALL_F_S_ARPACI_LARSEN 
CS_WALL_F_S_VDRIEST 
CS_WALL_F_S_LOUIS 
CS_WALL_F_S_MONIN_OBUKHOV 
CS_WALL_F_S_SMOOTH_ROUGH 

◆ cs_wall_f_type_t

enum cs_wall_f_type_t
Enumerator
CS_WALL_F_UNSET 
CS_WALL_F_DISABLED 
CS_WALL_F_1SCALE_POWER 
CS_WALL_F_1SCALE_LOG 
CS_WALL_F_2SCALES_LOG 
CS_WALL_F_SCALABLE_2SCALES_LOG 
CS_WALL_F_2SCALES_VDRIEST 
CS_WALL_F_2SCALES_SMOOTH_ROUGH 
CS_WALL_F_2SCALES_CONTINUOUS 

Function Documentation

◆ _dupdyp()

static cs_real_t _dupdyp ( cs_real_t  yp,
cs_real_t  ka,
cs_real_t  B,
cs_real_t  cuv,
cs_real_t  y0,
cs_real_t  n 
)
inlinestatic

◆ _uplus()

static cs_real_t _uplus ( cs_real_t  yp,
cs_real_t  ka,
cs_real_t  B,
cs_real_t  cuv,
cs_real_t  y0,
cs_real_t  n 
)
inlinestatic

◆ _vdriest_dupdyp_integral()

static cs_real_t _vdriest_dupdyp_integral ( cs_real_t  yplus)
inlinestatic

◆ cs_get_glob_wall_functions()

cs_wall_functions_t* cs_get_glob_wall_functions ( void  )

◆ cs_immersed_boundary_wall_functions()

void cs_immersed_boundary_wall_functions ( int  f_id,
cs_real_t *  st_exp,
cs_real_t *  st_imp 
)

Compute boundary contributions for all immersed boundaries.

Parameters
[in]f_idfield id of the variable
[out]st_expexplicit source term
[out]st_impimplicit part of the source term

This is similar to clptur.

Parameters
[in]f_idfield id of the variable
[out]st_expexplicit source term
[out]st_impimplicit part of the source term

◆ cs_wall_functions_1scale_log()

static void cs_wall_functions_1scale_log ( cs_real_t  l_visc,
cs_real_t  vel,
cs_real_t  y,
int *  iuntur,
cs_gnum_t *  nsubla,
cs_gnum_t *  nlogla,
cs_real_t *  ustar,
cs_real_t *  uk,
cs_real_t *  yplus,
cs_real_t *  ypup,
cs_real_t *  cofimp 
)
inlinestatic

Log law: piecewise linear and log, with one velocity scale based on the friction.

Parameters
[in]ifacface number
[in]l_visckinematic viscosity
[in]velwall projected cell center velocity
[in]ywall distance
[out]iunturindicator: 0 in the viscous sublayer
[out]nsublacounter of cell in the viscous sublayer
[out]nloglacounter of cell in the log-layer
[out]ustarfriction velocity
[out]ukfriction velocity
[out]yplusdimensionless distance to the wall
[out]ypupyplus projected vel ratio
[out]cofimp$\frac{|U_F|}{|U_I^p|}$ to ensure a good turbulence production

◆ cs_wall_functions_1scale_power()

static void cs_wall_functions_1scale_power ( cs_real_t  l_visc,
cs_real_t  vel,
cs_real_t  y,
int *  iuntur,
cs_gnum_t *  nsubla,
cs_gnum_t *  nlogla,
cs_real_t *  ustar,
cs_real_t *  uk,
cs_real_t *  yplus,
cs_real_t *  ypup,
cs_real_t *  cofimp 
)
inlinestatic

Power law: Werner & Wengle.

Parameters
[in]l_visckinematic viscosity
[in]velwall projected cell center velocity
[in]ywall distance
[out]iunturindicator: 0 in the viscous sublayer
[out]nsublacounter of cell in the viscous sublayer
[out]nloglacounter of cell in the log-layer
[out]ustarfriction velocity
[out]ukfriction velocity
[out]yplusdimensionless distance to the wall
[out]ypupyplus projected vel ratio
[out]cofimp$\frac{|U_F|}{|U_I^p|}$ to ensure a good turbulence production

◆ cs_wall_functions_2scales_continuous()

static void cs_wall_functions_2scales_continuous ( cs_real_t  rnnb,
cs_real_t  l_visc,
cs_real_t  t_visc,
cs_real_t  vel,
cs_real_t  y,
cs_real_t  kinetic_en,
int *  iuntur,
cs_gnum_t *  nsubla,
cs_gnum_t *  nlogla,
cs_real_t *  ustar,
cs_real_t *  uk,
cs_real_t *  yplus,
cs_real_t *  ypup,
cs_real_t *  cofimp 
)
inlinestatic

Continuous law of the wall between the linear and log law, with two velocity scales based on the friction and the turbulent kinetic energy. Can be used with RANS model either in high Reynolds or in low Reynolds (if the underlying RANS model is compatible).

Parameters
[in]rnnb$\vec{n}.(\tens{R}\vec{n})$
[in]l_visckinematic viscosity
[in]t_viscturbulent kinematic viscosity
[in]velwall projected cell center velocity
[in]ywall distance
[in]kinetic_enturbulent kinetic energy
[out]iunturindicator: 0 in the viscous sublayer
[out]nsublacounter of cell in the viscous sublayer
[out]nloglacounter of cell in the log-layer
[out]ustarfriction velocity
[out]ukfriction velocity
[out]yplusdimensionless distance to the wall
[out]ypupyplus projected vel ratio
[out]cofimp$\frac{|U_F|}{|U_I^p|}$ to ensure a good turbulence production

◆ cs_wall_functions_2scales_log()

static void cs_wall_functions_2scales_log ( cs_real_t  l_visc,
cs_real_t  t_visc,
cs_real_t  vel,
cs_real_t  y,
cs_real_t  kinetic_en,
int *  iuntur,
cs_gnum_t *  nsubla,
cs_gnum_t *  nlogla,
cs_real_t *  ustar,
cs_real_t *  uk,
cs_real_t *  yplus,
cs_real_t *  ypup,
cs_real_t *  cofimp 
)
inlinestatic

Log law: piecewise linear and log, with two velocity scales based on the friction and the turbulent kinetic energy.

Parameters
[in]l_visckinematic viscosity
[in]t_viscturbulent kinematic viscosity
[in]velwall projected cell center velocity
[in]ywall distance
[in]kinetic_enturbulent kinetic energy
[out]iunturindicator: 0 in the viscous sublayer
[out]nsublacounter of cell in the viscous sublayer
[out]nloglacounter of cell in the log-layer
[out]ustarfriction velocity
[out]ukfriction velocity
[out]yplusdimensionless distance to the wall
[out]ypupyplus projected vel ratio
[out]cofimp$\frac{|U_F|}{|U_I^p|}$ to ensure a good turbulence production

◆ cs_wall_functions_2scales_scalable()

static void cs_wall_functions_2scales_scalable ( cs_real_t  l_visc,
cs_real_t  t_visc,
cs_real_t  vel,
cs_real_t  y,
cs_real_t  kinetic_en,
int *  iuntur,
cs_gnum_t *  nsubla,
cs_gnum_t *  nlogla,
cs_real_t *  ustar,
cs_real_t *  uk,
cs_real_t *  yplus,
cs_real_t *  dplus,
cs_real_t *  ypup,
cs_real_t *  cofimp 
)
inlinestatic

Scalable wall function: shift the wall if $ y^+ < y^+_{lim} $.

Parameters
[in]l_visckinematic viscosity
[in]t_viscturbulent kinematic viscosity
[in]velwall projected cell center velocity
[in]ywall distance
[in]kinetic_enturbulent kinetic energy
[out]iunturindicator: 0 in the viscous sublayer
[out]nsublacounter of cell in the viscous sublayer
[out]nloglacounter of cell in the log-layer
[out]ustarfriction velocity
[out]ukfriction velocity
[out]yplusdimensionless distance to the wall
[out]dplusdimensionless shift to the wall for scalable wall functions
[out]ypupyplus projected vel ratio
[out]cofimp$\frac{|U_F|}{|U_I^p|}$ to ensure a good turbulence production

◆ cs_wall_functions_2scales_smooth_rough()

static void cs_wall_functions_2scales_smooth_rough ( cs_real_t  l_visc,
cs_real_t  t_visc,
cs_real_t  vel,
cs_real_t  y,
cs_real_t  rough_d,
cs_real_t  kinetic_en,
int *  iuntur,
cs_gnum_t *  nsubla,
cs_gnum_t *  nlogla,
cs_real_t *  ustar,
cs_real_t *  uk,
cs_real_t *  yplus,
cs_real_t *  dplus,
cs_real_t *  ypup,
cs_real_t *  cofimp 
)
inlinestatic

Two velocity scales wall function with automatic switch from rough to smooth.

$ u^+ $ is computed as follows:

\[ u^+ = \dfrac{1}{\kappa} \ln \left(\dfrac{(y+y_0) u_k}{\nu + \alpha \xi u_k} \right) + Cst_{smooth} \]

with $ \alpha = \exp \left(- \kappa(Cst_{rough}-Cst_{smooth})\right) \simeq 0.26 $ and $ y_0 = \alpha \xi \exp \left(-\kappa Cst_{smooth} \right) = \xi \exp \left(-\kappa Cst_{rough} \right) \simeq \dfrac{\xi}{33}$.

Parameters
[in]l_visckinematic viscosity
[in]t_viscturbulent kinematic viscosity
[in]velwall projected cell center velocity
[in]ywall distance
[in]rough_droughness length scale (not sand grain)
[in]kinetic_enturbulent kinetic energy
[out]iunturindicator: 0 in the viscous sublayer
[out]nsublacounter of cell in the viscous sublayer
[out]nloglacounter of cell in the log-layer
[out]ustarfriction velocity
[out]ukfriction velocity
[out]yplusdimensionless distance to the wall
[out]dplusdimensionless shift to the wall for scalable wall functions
[out]ypupyplus projected vel ratio
[out]cofimp$\frac{|U_F|}{|U_I^p|}$ to ensure a good turbulence production

◆ cs_wall_functions_2scales_vdriest()

static void cs_wall_functions_2scales_vdriest ( cs_real_t  rnnb,
cs_real_t  l_visc,
cs_real_t  vel,
cs_real_t  y,
cs_real_t  kinetic_en,
int *  iuntur,
cs_gnum_t *  nsubla,
cs_gnum_t *  nlogla,
cs_real_t *  ustar,
cs_real_t *  uk,
cs_real_t *  yplus,
cs_real_t *  ypup,
cs_real_t *  cofimp,
cs_real_t *  lmk,
cs_real_t  kr,
bool  wf 
)
inlinestatic

Two velocity scales wall function using Van Driest mixing length.

$ u^+ $ is computed as follows:

\[ u^+ = \int_0^{y_k^+} \dfrac{dy_k^+}{1+L_m^k} \]

with $ L_m^k $ standing for Van Driest mixing length:

\[ L_m^k = \kappa y_k^+ (1 - exp(\dfrac{-y_k^+}{A})) \]

.

A polynome fitting the integral is used for $ y_k^+ < 200 $, and a log law is used for $ y_k^+ >= 200 $.

A wall roughness can be taken into account in the mixing length as proposed by Rotta (1962) with Cebeci & Chang (1978) correlation.

Parameters
[in]rnnb$\vec{n}.(\tens{R}\vec{n})$
[in]l_visckinematic viscosity
[in]velwall projected cell center velocity
[in]ywall distance
[in]kinetic_enturbulent kinetic energy
[out]iunturindicator: 0 in the viscous sublayer
[out]nsublacounter of cell in the viscous sublayer
[out]nloglacounter of cell in the log-layer
[out]ustarfriction velocity
[out]ukfriction velocity
[out]yplusdimensionless distance to the wall
[out]ypupyplus projected vel ratio
[out]cofimp$\frac{|U_F|}{|U_I^p|}$ to ensure a good turbulence production
[in]lmkdimensionless mixing length
[in]krwall roughness
[in]wfenable full wall function computation, if false, uk is not recomputed and uplus is the only output

◆ cs_wall_functions_disabled()

static void cs_wall_functions_disabled ( cs_real_t  l_visc,
cs_real_t  t_visc,
cs_real_t  vel,
cs_real_t  y,
int *  iuntur,
cs_gnum_t *  nsubla,
cs_gnum_t *  nlogla,
cs_real_t *  ustar,
cs_real_t *  uk,
cs_real_t *  yplus,
cs_real_t *  dplus,
cs_real_t *  ypup,
cs_real_t *  cofimp 
)
inlinestatic

No wall function.

Parameters
[in]l_visckinematic viscosity
[in]t_viscturbulent kinematic viscosity
[in]velwall projected cell center velocity
[in]ywall distance
[out]iunturindicator: 0 in the viscous sublayer
[out]nsublacounter of cell in the viscous sublayer
[out]nloglacounter of cell in the log-layer
[out]ustarfriction velocity
[out]ukfriction velocity
[out]yplusdimensionless distance to the wall
[out]dplusdimensionless shift to the wall for scalable wall functions
[out]ypupyplus projected vel ratio
[out]cofimp$\frac{|U_F|}{|U_I^p|}$ to ensure a good turbulence production

◆ cs_wall_functions_s_arpaci_larsen()

static void cs_wall_functions_s_arpaci_larsen ( cs_real_t  l_visc,
cs_real_t  prl,
cs_real_t  prt,
cs_real_t  rough_t,
cs_real_t  uk,
cs_real_t  yplus,
cs_real_t  dplus,
cs_real_t *  htur,
cs_real_t *  yplim 
)
inlinestatic

The correction of the exchange coefficient is computed thanks to a similarity model between dynamic viscous sub-layer and themal sub-layer.

$ T^+ $ is computed as follows:

  • For a laminar Prandtl number smaller than 0.1 (such as liquid metals), the standard model with two sub-layers (Prandtl-Taylor) is used.
  • For a laminar Prandtl number larger than 0.1 (such as liquids and gas), a model with three sub-layers (Arpaci-Larsen) is used.

The final exchange coefficient is:

\[ h = \dfrac{K}{\centip \centf} h_{tur} \]

Parameters
[in]l_visckinetic viscosity
[in]prllaminar Prandtl number
[in]prtturbulent Prandtl number
[in]rough_tscalar roughness length scale
[in]ukvelocity scale based on TKE
[in]yplusdimensionless distance to the wall
[out]dplusdimensionless shift to the wall for scalable wall functions
[out]hturcorrection for the exchange coefficient ( $ Pr y^+/T^+ $)
[out]yplimvalue of the limit for $ y^+ $

◆ cs_wall_functions_s_smooth_rough()

static void cs_wall_functions_s_smooth_rough ( cs_real_t  l_visc,
cs_real_t  prl,
cs_real_t  prt,
cs_real_t  rough_t,
cs_real_t  uk,
cs_real_t  yplus,
cs_real_t  dplus,
cs_real_t *  htur 
)
inlinestatic

Rough Smooth Thermal Wall Function - Prototype.

Parameters
[in]l_visckinetic viscosity
[in]prlmolecular Prandtl number ( $ Pr=\sigma=\frac{\mu C_p}{\lambda_f} $ )
[in]prtturbulent Prandtl number ( $ \sigma_t $ )
[in]rough_tscalar roughness length scale
[in]ukvelocity scale based on TKE
[in]yplusdimensionless distance to the wall
[in]dplusdimensionless shift to the wall for scalable wall function
[out]hturcorrection for the exchange coefficient ( $ Pr y^+/T^+ $)

◆ cs_wall_functions_s_vdriest()

static void cs_wall_functions_s_vdriest ( cs_real_t  prl,
cs_real_t  prt,
cs_real_t  yplus,
cs_real_t *  htur 
)
inlinestatic

The correction of the exchange coefficient $ h_{tur} = \sigma \dfrac{y^+}{t^+} $ is computed thanks to a numerical integration of:

\[ \dfrac{T^+}{\sigma} = \int_0^{y_k^+} \dfrac{dy_k^+}{1+\dfrac{\sigma}{\sigma_t}\nu_t^+} \]

with $ \nu_t^+ = L_m^k $ as assumed in the derivation of the two scales wall function using Van Driest mixing length. Therefore $ L_m^k = \kappa y_k^+(1 - exp(\dfrac{-y_k^+}{A})) $ is taken.

Notice that we integrate up to $ y^+=100 $ (YP100), beyond that value the profile is prolonged by a logarithm relying on the fact that $ \nu_t^+=\kappa y^+ $ beyond $ y^+=100 $.

Parameters
[in]prlmolecular Prandtl number ( $ Pr=\sigma=\frac{\mu C_p}{\lambda_f} $ )
[in]prtturbulent Prandtl number ( $ \sigma_t $ )
[in]yplusdimensionless distance to the wall
[out]hturcorrection for the exchange coefficient ( $ Pr y^+/T^+ $)

◆ cs_wall_functions_scalar()

void cs_wall_functions_scalar ( cs_wall_f_s_type_t  iwalfs,
cs_real_t  l_visc,
cs_real_t  prl,
cs_real_t  prt,
cs_real_t  rough_t,
cs_real_t  uk,
cs_real_t  yplus,
cs_real_t  dplus,
cs_real_t *  htur,
cs_real_t *  yplim 
)

Compute the correction of the exchange coefficient between the fluid and the wall for a turbulent flow.

This is function of the dimensionless distance to the wall $ y^+ = \dfrac{\centip \centf u_\star}{\nu}$.

Then the return coefficient reads:

\[ h_{tur} = Pr \dfrac{y^+}{T^+} \]

Parameters
[in]iwalfstype of wall functions for scalar
[in]l_visckinematic viscosity
[in]prllaminar Prandtl number
[in]prtturbulent Prandtl number
[in]rough_tscalar roughness lenghth scale
[in]ukvelocity scale based on TKE
[in]yplusdimensionless distance to the wall
[in]dplusdimensionless distance for scalable wall functions
[out]hturcorrected exchange coefficient
[out]yplimvalue of the limit for $ y^+ $

◆ cs_wall_functions_velocity()

void cs_wall_functions_velocity ( cs_wall_f_type_t  iwallf,
cs_real_t  l_visc,
cs_real_t  t_visc,
cs_real_t  vel,
cs_real_t  y,
cs_real_t  rough_d,
cs_real_t  rnnb,
cs_real_t  kinetic_en,
int *  iuntur,
cs_gnum_t *  nsubla,
cs_gnum_t *  nlogla,
cs_real_t *  ustar,
cs_real_t *  uk,
cs_real_t *  yplus,
cs_real_t *  ypup,
cs_real_t *  cofimp,
cs_real_t *  dplus 
)

Compute the friction velocity and $y^+$ / $u^+$.

Parameters
[in]iwallfwall function type
[in]l_visckinematic viscosity
[in]t_viscturbulent kinematic viscosity
[in]velwall projected cell center velocity
[in]ywall distance
[in]rough_droughness lenghth scale
[in]rnnb$\vec{n}.(\tens{R}\vec{n})$
[in]kinetic_enturbulent kinetic energy
[in]iunturindicator: 0 in the viscous sublayer
[in]nsublacounter of cell in the viscous sublayer
[in]nloglacounter of cell in the log-layer
[out]ustarfriction velocity
[out]ukfriction velocity
[out]yplusnon-dimension wall distance
[out]ypupyplus projected vel ratio
[out]cofimp$\frac{|U_F|}{|U_I^p|}$ to ensure a good turbulence production
[out]dplusdimensionless shift to the wall for scalable wall functions
[in]iwallfwall function type
[in]l_visckinematic viscosity
[in]t_viscturbulent kinematic viscosity
[in]velwall projected cell center velocity
[in]ywall distance
[in]rough_droughness length scale (not sand grain roughness)
[in]rnnb$\vec{n}.(\tens{R}\vec{n})$
[in]kinetic_enturbulent kinetic energy (cell center)
[in,out]iunturindicator: 0 in the viscous sublayer
[in,out]nsublacounter of cell in the viscous sublayer
[in,out]nloglacounter of cell in the log-layer
[out]ustarfriction velocity
[out]ukfriction velocity
[out]yplusdimensionless distance to the wall
[out]ypupyplus projected vel ratio
[out]cofimp$\frac{|U_F|}{|U_I^p|}$ to ensure a good turbulence production
[out]dplusdimensionless shift to the wall for scalable wall functions

◆ hturbp()

void hturbp ( const int *const  iwalfs,
const cs_real_t *const  l_visc,
const cs_real_t *const  prl,
const cs_real_t *const  prt,
const cs_real_t *const  rough_t,
const cs_real_t *const  uk,
const cs_real_t *const  yplus,
const cs_real_t *const  dplus,
cs_real_t *  htur,
cs_real_t *  yplim 
)

◆ wallfunctions()

void wallfunctions ( const int *const  iwallf,
const cs_lnum_t *const  ifac,
const cs_real_t *const  viscosity,
const cs_real_t *const  t_visc,
const cs_real_t *const  vel,
const cs_real_t *const  y,
const cs_real_t *const  rough_d,
const cs_real_t *const  rnnb,
const cs_real_t *const  kinetic_en,
int *  iuntur,
cs_lnum_t *  nsubla,
cs_lnum_t *  nlogla,
cs_real_t *  ustar,
cs_real_t *  uk,
cs_real_t *  yplus,
cs_real_t *  ypup,
cs_real_t *  cofimp,
cs_real_t *  dplus 
)

Variable Documentation

◆ cs_glob_wall_functions

const cs_wall_functions_t* cs_glob_wall_functions
extern