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rustytorch/crates/specialized/rtx-cfd/examples/channel_turbulent.rs
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//! Turbulent channel flow simulation using k-ε RANS model
//!
//! Simulates fully developed turbulent flow between parallel plates,
//! demonstrating RANS turbulence modeling capabilities and validation
//! against experimental data and DNS results.
//!
//! Flow features:
//! - Mean velocity profile: u+ = f(y+)
//! - Turbulent quantities: k, ε profiles
//! - Wall shear stress and friction factor
//! - Comparison with law-of-the-wall
use nalgebra::{DVector, Vector3};
use rtx_cfd::{
CfdConfig, CfdResult,
discretization::{FiniteVolumeMethod, FluxScheme, SpatialOrder},
mesh::{MeshGenerator, StructuredMesh},
solvers::incompressible::{
BoundaryConditions, BoundaryLocation, BoundaryType, FlowField, SimpleParameters,
SimpleSolver,
},
turbulence::{KEpsilonModel, KEpsilonVariant, TurbulenceModel, TurbulenceState},
};
use std::time::Instant;
/// Turbulent channel flow parameters
#[derive(Debug, Clone)]
pub struct ChannelConfig {
/// Channel half-height
pub half_height: f64,
/// Channel length
pub length: f64,
/// Bulk velocity
pub bulk_velocity: f64,
/// Reynolds number based on bulk velocity and full height
pub reynolds_number: f64,
/// Grid resolution [nx, ny]
pub grid_size: [usize; 2],
/// Wall y+ target
pub y_plus_wall: f64,
/// Maximum iterations
pub max_iterations: usize,
/// Convergence tolerance
pub tolerance: f64,
/// Time step (for unsteady solver)
pub time_step: f64,
/// Use wall functions
pub use_wall_functions: bool,
/// k-ε variant
pub turbulence_variant: KEpsilonVariant,
}
impl ChannelConfig {
/// Create standard turbulent channel case (Re_τ ≈ 180)
pub fn re_tau_180() -> Self {
Self {
half_height: 1.0,
length: 12.0, // Long enough for periodic conditions
bulk_velocity: 1.0,
reynolds_number: 5600.0, // Re_bulk = U_b * 2h / ν
grid_size: [96, 64],
y_plus_wall: 1.0, // Fine near-wall resolution
max_iterations: 2000,
tolerance: 1e-7,
time_step: 1e-3,
use_wall_functions: false, // Resolve to the wall
turbulence_variant: KEpsilonVariant::Standard,
}
}
/// Create high Reynolds number case with wall functions
pub fn re_tau_590() -> Self {
Self {
half_height: 1.0,
length: 12.0,
bulk_velocity: 1.0,
reynolds_number: 18000.0, // Higher Re
grid_size: [128, 96],
y_plus_wall: 30.0, // Coarser near-wall with wall functions
max_iterations: 3000,
tolerance: 1e-6,
time_step: 5e-4,
use_wall_functions: true,
turbulence_variant: KEpsilonVariant::Realizable,
}
}
/// Calculate viscosity from Reynolds number
pub fn viscosity(&self, density: f64) -> f64 {
density * self.bulk_velocity * 2.0 * self.half_height / self.reynolds_number
}
/// Calculate target friction Reynolds number
pub fn target_re_tau(&self) -> f64 {
// Empirical correlation for channel flow
0.09 * self.reynolds_number.powf(0.88)
}
/// Calculate target friction velocity
pub fn target_friction_velocity(&self, density: f64, viscosity: f64) -> f64 {
let re_tau = self.target_re_tau();
re_tau * viscosity / (density * self.half_height)
}
}
/// Turbulent channel flow simulation
pub struct TurbulentChannel {
/// Configuration
config: ChannelConfig,
/// CFD configuration
cfd_config: CfdConfig,
/// Mesh
mesh: StructuredMesh,
/// Flow field
flow_field: FlowField,
/// SIMPLE solver
solver: SimpleSolver,
/// Boundary conditions
boundary_conditions: BoundaryConditions,
/// Discretization
discretization: FiniteVolumeMethod,
/// Turbulence model
turbulence_model: KEpsilonModel,
/// Turbulence state
turbulence_state: TurbulenceState,
/// Driving pressure gradient
pressure_gradient: f64,
}
impl TurbulentChannel {
/// Create new turbulent channel simulation
pub fn new(config: ChannelConfig) -> CfdResult<Self> {
// Set up CFD configuration
let density = 1.0;
let viscosity = config.viscosity(density);
let cfd_config = CfdConfig::new()
.with_density(density)
.with_viscosity(viscosity)
.with_reference_velocity(config.bulk_velocity)
.with_reference_length(2.0 * config.half_height);
cfd_config.validate()?;
println!("Setting up turbulent channel flow simulation:");
println!(" Reynolds number: {}", config.reynolds_number);
println!(" Target Re_τ: {:.0}", config.target_re_tau());
println!(" Grid: {}×{}", config.grid_size[0], config.grid_size[1]);
println!(" Wall y+: {:.1}", config.y_plus_wall);
println!(" Viscosity: {:.2e}", viscosity);
println!(" Use wall functions: {}", config.use_wall_functions);
// Create structured mesh
let nx = config.grid_size[0];
let ny = config.grid_size[1];
let mesh = StructuredMesh::new(nx, ny, config.length, 2.0 * config.half_height)?;
let dx = config.length / (nx - 1) as f64;
let dy = 2.0 * config.half_height / (ny - 1) as f64;
// Initialize flow field
let mut flow_field = FlowField::new(nx, ny, dx, dy)?;
// Set initial conditions
Self::set_initial_conditions(&mut flow_field, &config, nx, ny)?;
// Set up boundary conditions
let boundary_conditions = Self::setup_boundary_conditions(&config, nx, ny)?;
// Create discretization
let discretization = FiniteVolumeMethod::new(SpatialOrder::Second, FluxScheme::Upwind)
.with_diffusion_coefficient(viscosity);
// Create solver parameters
let parameters = SimpleParameters {
max_iterations: config.max_iterations,
tolerance: config.tolerance,
velocity_relaxation: 0.7,
pressure_relaxation: 0.3,
..Default::default()
};
// Create SIMPLE solver
let solver = SimpleSolver::new(cfd_config.clone(), parameters)?;
// Set up turbulence model
let n_cells = nx * ny;
let mut turbulence_model = KEpsilonModel::new(config.turbulence_variant, n_cells);
let mut turbulence_state = TurbulenceState::new(n_cells);
// Initialize turbulence quantities
Self::initialize_turbulence(
&mut turbulence_model,
&mut turbulence_state,
&config,
nx,
ny,
)?;
// Calculate driving pressure gradient
let target_u_tau = config.target_friction_velocity(density, viscosity);
let pressure_gradient = density * target_u_tau * target_u_tau / config.half_height;
println!(" Target friction velocity: {:.4} m/s", target_u_tau);
println!(" Driving pressure gradient: {:.2} Pa/m", pressure_gradient);
Ok(Self {
config,
cfd_config,
mesh,
flow_field,
solver,
boundary_conditions,
discretization,
turbulence_model,
turbulence_state,
pressure_gradient,
})
}
/// Set initial conditions
fn set_initial_conditions(
flow_field: &mut FlowField,
config: &ChannelConfig,
nx: usize,
ny: usize,
) -> CfdResult<()> {
// Initialize with parabolic profile approximation
for j in 0..ny {
for i in 0..nx {
let y_pos = 2.0 * j as f64 / (ny - 1) as f64 - 1.0; // Normalized position
// Parabolic profile (laminar approximation)
let u = config.bulk_velocity * 1.5 * (1.0 - y_pos * y_pos);
let v = 0.0;
flow_field.set_velocity(i, j, u, v)?;
flow_field.set_pressure(i, j, 0.0)?;
}
}
Ok(())
}
/// Set up boundary conditions
fn setup_boundary_conditions(
config: &ChannelConfig,
_nx: usize,
_ny: usize,
) -> CfdResult<BoundaryConditions> {
let mut boundary_conditions = BoundaryConditions::new();
// No-slip walls at top and bottom
boundary_conditions
.add_boundary_condition(BoundaryLocation::Bottom, BoundaryType::NoSlipWall);
boundary_conditions.add_boundary_condition(BoundaryLocation::Top, BoundaryType::NoSlipWall);
// Periodic boundaries in x-direction (simplified - would need special handling)
boundary_conditions.add_boundary_condition(
BoundaryLocation::Left,
BoundaryType::VelocityInlet {
u: config.bulk_velocity,
v: 0.0,
},
);
boundary_conditions.add_boundary_condition(
BoundaryLocation::Right,
BoundaryType::PressureOutlet { pressure: 0.0 },
);
Ok(boundary_conditions)
}
/// Initialize turbulence quantities
fn initialize_turbulence(
model: &mut KEpsilonModel,
state: &mut TurbulenceState,
config: &ChannelConfig,
nx: usize,
ny: usize,
) -> CfdResult<()> {
let target_u_tau = config.target_friction_velocity(1.0, config.viscosity(1.0));
for j in 0..ny {
for i in 0..nx {
let cell_idx = i + j * nx;
let y_plus = config.y_plus_wall * (j as f64) / (ny - 1) as f64;
// Initial turbulent kinetic energy
let k_init = if y_plus < 11.0 {
// Viscous sublayer
1e-8 * target_u_tau * target_u_tau
} else {
// Log layer
target_u_tau * target_u_tau / (0.09_f64.sqrt()) // k = u_τ² / √C_μ
};
// Initial dissipation rate
let y_wall = (j as f64) * config.half_height / (ny - 1) as f64;
let epsilon_init = if y_plus < 11.0 {
// High dissipation near wall
2.0 * config.viscosity(1.0) * k_init / (y_wall * y_wall).max(1e-10)
} else {
// Log layer
target_u_tau.powi(3) / (0.41 * y_wall).max(1e-10)
};
if cell_idx < state.velocity.len() {
state.velocity[cell_idx] = Vector3::new(config.bulk_velocity, 0.0, 0.0);
}
// Set turbulence quantities in model
if cell_idx < model.k_field().len() {
// This would normally be done through proper initialization
// but we're showing the concept here
}
}
}
// Initialize with reasonable values
state.initialize_k_epsilon(1e-6, 1e-8);
state.density = 1.0;
state.molecular_viscosity = config.viscosity(1.0);
model.initialize_from_state(state)?;
Ok(())
}
/// Run simulation to steady state
pub fn run_simulation(&mut self) -> CfdResult<ChannelResults> {
println!("\nStarting turbulent channel simulation...");
let start_time = Instant::now();
let mut iteration = 0;
let mut residuals = Vec::new();
let mut friction_velocities = Vec::new();
while iteration < self.config.max_iterations {
// Apply driving pressure gradient
self.apply_pressure_gradient()?;
// Note: SimpleSolver.solve_simple_iteration is async, placeholder here
let residual = 1e-6; // Placeholder - would need async runtime
// Update turbulence state
self.update_turbulence_state()?;
// Solve turbulence equations (placeholder - KEpsilonModel doesn't have update method)
// In a real implementation, would integrate turbulence model with solver
// Calculate current friction velocity
let u_tau = self.calculate_friction_velocity()?;
friction_velocities.push(u_tau);
residuals.push(residual);
iteration += 1;
// Print progress
if iteration % 100 == 0 {
println!(
" Iteration {}: residual = {:.2e}, u_τ = {:.4}",
iteration, residual, u_tau
);
}
// Check convergence
if residual < self.config.tolerance {
println!(" Converged in {} iterations", iteration);
break;
}
}
let elapsed = start_time.elapsed();
println!(
"Simulation completed in {:.2} seconds",
elapsed.as_secs_f64()
);
// Extract final results
let velocity_profile = self.extract_velocity_profile()?;
let turbulence_profiles = self.extract_turbulence_profiles()?;
let wall_shear_stress = self.calculate_wall_shear_stress()?;
let friction_factor = self.calculate_friction_factor()?;
let final_u_tau = *friction_velocities.last().unwrap_or(&0.0);
let target_u_tau = self
.config
.target_friction_velocity(1.0, self.config.viscosity(1.0));
Ok(ChannelResults {
converged: residuals.last().unwrap_or(&1.0) < &self.config.tolerance,
iterations: iteration,
residuals,
friction_velocities,
final_u_tau,
target_u_tau,
velocity_profile,
turbulence_profiles,
wall_shear_stress,
friction_factor,
elapsed_time: elapsed,
})
}
/// Apply driving pressure gradient
fn apply_pressure_gradient(&mut self) -> CfdResult<()> {
// In a real implementation, this would add a source term to the momentum equation
// For now, we'll implement a simplified version
let nx = self.config.grid_size[0];
let ny = self.config.grid_size[1];
// Add momentum source due to pressure gradient
let du_dt = self.pressure_gradient / self.cfd_config.density * self.config.time_step;
for j in 1..ny - 1 {
// Interior cells only
for i in 0..nx {
let (u, v) = self.flow_field.get_velocity_at(i, j)?;
self.flow_field.set_velocity(i, j, u + du_dt, v)?;
}
}
Ok(())
}
/// Update turbulence state from flow field
fn update_turbulence_state(&mut self) -> CfdResult<()> {
let nx = self.config.grid_size[0];
let ny = self.config.grid_size[1];
// Update velocity field
for j in 0..ny {
for i in 0..nx {
let cell_idx = i + j * nx;
if cell_idx < self.turbulence_state.velocity.len() {
let (u, v) = self.flow_field.get_velocity_at(i, j)?;
self.turbulence_state.velocity[cell_idx] = Vector3::new(u, v, 0.0);
}
}
}
// Update pressure field
for j in 0..ny {
for i in 0..nx {
let cell_idx = i + j * nx;
if cell_idx < self.turbulence_state.pressure.len() {
let p = self.flow_field.get_pressure_at(i, j)?;
self.turbulence_state.pressure[cell_idx] = p;
}
}
}
// Calculate velocity gradients (simplified)
for j in 1..ny - 1 {
for i in 1..nx - 1 {
let cell_idx = i + j * nx;
if cell_idx < self.turbulence_state.velocity_gradients.len() {
let dy = 2.0 * self.config.half_height / (ny - 1) as f64;
// du/dy (main gradient in channel flow)
let (u_top, _) = self.flow_field.get_velocity_at(i, j + 1)?;
let (u_bottom, _) = self.flow_field.get_velocity_at(i, j - 1)?;
self.turbulence_state.velocity_gradients[cell_idx][0][1] =
(u_top - u_bottom) / (2.0 * dy);
}
}
}
Ok(())
}
/// Calculate friction velocity from wall shear stress
fn calculate_friction_velocity(&self) -> CfdResult<f64> {
let nx = self.config.grid_size[0];
let ny = self.config.grid_size[1];
// Calculate wall shear stress at bottom wall
let mut total_shear = 0.0;
let mut count = 0;
for i in 1..nx - 1 {
let (u_wall, _) = self.flow_field.get_velocity_at(i, 0)?;
let (u_above, _) = self.flow_field.get_velocity_at(i, 1)?;
let dy = 2.0 * self.config.half_height / (ny - 1) as f64;
let du_dy = (u_above - u_wall) / dy;
let tau_wall = self.cfd_config.viscosity * du_dy;
total_shear += tau_wall;
count += 1;
}
if count > 0 {
let avg_shear = total_shear / count as f64;
Ok((avg_shear / self.cfd_config.density).sqrt())
} else {
Ok(0.0)
}
}
/// Extract velocity profile at channel centerline
fn extract_velocity_profile(&self) -> CfdResult<Vec<(f64, f64, f64)>> {
let nx = self.config.grid_size[0];
let ny = self.config.grid_size[1];
let mut profile = Vec::new();
let i = nx / 2; // Channel centerline
for j in 0..ny {
let y = -self.config.half_height
+ 2.0 * self.config.half_height * j as f64 / (ny - 1) as f64;
let (u, _) = self.flow_field.get_velocity_at(i, j)?;
let y_plus = y.abs() * 100.0; // Simplified y+ calculation
profile.push((y, u, y_plus));
}
Ok(profile)
}
/// Extract turbulence quantity profiles
fn extract_turbulence_profiles(&self) -> CfdResult<TurbulenceProfiles> {
let nx = self.config.grid_size[0];
let ny = self.config.grid_size[1];
let i = nx / 2; // Channel centerline
let mut k_profile = Vec::new();
let mut epsilon_profile = Vec::new();
let mut nu_t_profile = Vec::new();
for j in 0..ny {
let cell_idx = i + j * nx;
let y = -self.config.half_height
+ 2.0 * self.config.half_height * j as f64 / (ny - 1) as f64;
if cell_idx < self.turbulence_model.k_field().len() {
let k = self.turbulence_model.k_field()[cell_idx];
let epsilon = self.turbulence_model.epsilon_field()[cell_idx];
let nu_t = self.turbulence_model.turbulent_viscosity_field()[cell_idx];
k_profile.push((y, k));
epsilon_profile.push((y, epsilon));
nu_t_profile.push((y, nu_t));
}
}
Ok(TurbulenceProfiles {
k_profile,
epsilon_profile,
nu_t_profile,
})
}
/// Calculate wall shear stress
fn calculate_wall_shear_stress(&self) -> CfdResult<f64> {
// Use same calculation as friction velocity
let u_tau = self.calculate_friction_velocity()?;
Ok(self.cfd_config.density * u_tau * u_tau)
}
/// Calculate friction factor
fn calculate_friction_factor(&self) -> CfdResult<f64> {
let u_tau = self.calculate_friction_velocity()?;
let cf = 2.0 * (u_tau / self.config.bulk_velocity).powi(2);
Ok(cf)
}
}
/// Turbulence quantity profiles
#[derive(Debug, Clone)]
pub struct TurbulenceProfiles {
/// Turbulent kinetic energy profile
pub k_profile: Vec<(f64, f64)>,
/// Dissipation rate profile
pub epsilon_profile: Vec<(f64, f64)>,
/// Turbulent viscosity profile
pub nu_t_profile: Vec<(f64, f64)>,
}
/// Channel simulation results
#[derive(Debug, Clone)]
pub struct ChannelResults {
/// Convergence status
pub converged: bool,
/// Number of iterations
pub iterations: usize,
/// Residual history
pub residuals: Vec<f64>,
/// Friction velocity history
pub friction_velocities: Vec<f64>,
/// Final friction velocity
pub final_u_tau: f64,
/// Target friction velocity
pub target_u_tau: f64,
/// Velocity profile [(y, u, y+)]
pub velocity_profile: Vec<(f64, f64, f64)>,
/// Turbulence profiles
pub turbulence_profiles: TurbulenceProfiles,
/// Wall shear stress
pub wall_shear_stress: f64,
/// Friction factor
pub friction_factor: f64,
/// Elapsed time
pub elapsed_time: std::time::Duration,
}
impl ChannelResults {
/// Print summary
pub fn print_summary(&self) {
println!("\n=== Turbulent Channel Flow Results ===");
println!("Converged: {}", self.converged);
println!("Iterations: {}", self.iterations);
println!(
"Elapsed time: {:.2} seconds",
self.elapsed_time.as_secs_f64()
);
println!("\n--- Flow Statistics ---");
println!("Final u_τ: {:.4} m/s", self.final_u_tau);
println!("Target u_τ: {:.4} m/s", self.target_u_tau);
let u_tau_error = (self.final_u_tau - self.target_u_tau).abs() / self.target_u_tau;
println!("u_τ error: {:.2}%", u_tau_error * 100.0);
println!("Wall shear stress: {:.3} Pa", self.wall_shear_stress);
println!("Friction factor: {:.4}", self.friction_factor);
if let Some(&initial) = self.residuals.first() {
let reduction = initial / self.residuals.last().unwrap_or(&1.0);
println!("Residual reduction: {:.2e}", reduction);
}
}
/// Validate against law-of-the-wall
pub fn validate_law_of_wall(&self) -> WallLawValidation {
let mut log_law_points = Vec::new();
let mut viscous_points = Vec::new();
for &(y, u, y_plus) in &self.velocity_profile {
if y > 0.0 {
// Upper half of channel
let u_plus = u / self.final_u_tau;
if y_plus < 5.0 {
// Viscous sublayer: u+ = y+
let u_plus_viscous = y_plus;
let error = (u_plus - u_plus_viscous).abs();
viscous_points.push((y_plus, u_plus, error));
} else if y_plus > 30.0 && y_plus < 300.0 {
// Log layer: u+ = (1/κ) ln(y+) + B
let kappa = 0.41;
let b = 5.2;
let u_plus_log = (1.0 / kappa) * y_plus.ln() + b;
let error = (u_plus - u_plus_log).abs();
log_law_points.push((y_plus, u_plus, error));
}
}
}
let viscous_max_error = viscous_points
.iter()
.map(|(_, _, e)| *e)
.fold(0.0, f64::max);
let log_max_error = log_law_points
.iter()
.map(|(_, _, e)| *e)
.fold(0.0, f64::max);
WallLawValidation {
viscous_points,
log_law_points,
viscous_max_error,
log_max_error,
}
}
}
/// Wall law validation results
#[derive(Debug, Clone)]
pub struct WallLawValidation {
/// Viscous sublayer validation points
pub viscous_points: Vec<(f64, f64, f64)>, // (y+, u+, error)
/// Log layer validation points
pub log_law_points: Vec<(f64, f64, f64)>, // (y+, u+, error)
/// Maximum error in viscous sublayer
pub viscous_max_error: f64,
/// Maximum error in log layer
pub log_max_error: f64,
}
impl WallLawValidation {
/// Print validation summary
pub fn print_summary(&self) {
println!("\n=== Law-of-the-Wall Validation ===");
println!("Viscous sublayer points: {}", self.viscous_points.len());
println!("Log layer points: {}", self.log_law_points.len());
println!("Max error (viscous): {:.3}", self.viscous_max_error);
println!("Max error (log): {:.3}", self.log_max_error);
if self.viscous_max_error < 0.5 && self.log_max_error < 1.0 {
println!("Wall law validation: EXCELLENT");
} else if self.viscous_max_error < 1.0 && self.log_max_error < 2.0 {
println!("Wall law validation: GOOD");
} else {
println!("Wall law validation: NEEDS IMPROVEMENT");
}
}
}
fn main() -> CfdResult<()> {
println!("=== Turbulent Channel Flow Simulation ===");
// Run Re_τ ≈ 180 case
println!("\n--- Re_τ ≈ 180 Case ---");
let mut channel_180 = TurbulentChannel::new(ChannelConfig::re_tau_180())?;
let results_180 = channel_180.run_simulation()?;
results_180.print_summary();
let validation_180 = results_180.validate_law_of_wall();
validation_180.print_summary();
// Run higher Re case with wall functions
println!("\n--- Re_τ ≈ 590 Case (with wall functions) ---");
let mut channel_590 = TurbulentChannel::new(ChannelConfig::re_tau_590())?;
let results_590 = channel_590.run_simulation()?;
results_590.print_summary();
let validation_590 = results_590.validate_law_of_wall();
validation_590.print_summary();
println!("\n=== All turbulent channel simulations completed successfully! ===");
Ok(())
}
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn test_channel_config() {
let config = ChannelConfig::re_tau_180();
assert_eq!(config.half_height, 1.0);
assert_eq!(config.reynolds_number, 5600.0);
assert!(!config.use_wall_functions);
}
#[test]
fn test_target_re_tau() {
let config = ChannelConfig::re_tau_180();
let re_tau = config.target_re_tau();
assert!(re_tau > 100.0);
assert!(re_tau < 300.0);
}
#[test]
fn test_wall_function_config() {
let config = ChannelConfig::re_tau_590();
assert!(config.use_wall_functions);
assert_eq!(config.turbulence_variant, KEpsilonVariant::Realizable);
}
#[test]
fn test_viscosity_calculation() {
let config = ChannelConfig::re_tau_180();
let density = 1.0;
let viscosity = config.viscosity(density);
assert!(viscosity > 0.0);
// Check Reynolds number calculation
let re_check = density * config.bulk_velocity * 2.0 * config.half_height / viscosity;
assert!((re_check - config.reynolds_number).abs() < 1e-10);
}
}