One Dimensional Numerical River Modeling overview of HEC-RAS calculation procedures Photo courtesy of California DWR

What we will coverReview of basic open channel flow conceptsHow HEC-RAS calculates water surface profilesData required for river models

Water Surface Profile CalculationsBasic Open Channel Flow ConceptsEnergy PrinciplesCross Section Subdivision for ConveyanceComputational ProcedureCritical Depth DeterminationMomentum EquationCross Section Spacing1D Model Limitations

The Energy Equation

Velocity DistributionFactors influencing velocity distribution:Shape of the cross sectionRoughness of the boundariesPresence of bendsContractions and expansionsFlow obstructions, such as bridge piers, etcUse a to account for kinetic energy for cross section

Kinetic Energy Head for a Cross Section12A1, Q1A2, Q2

Energy LossesFor steady flow two types of losses are taken into account:Friction Contraction and Expansion

For unsteady flow only friction loss is used

Cross Section Subdivision for Conveyance CalculationsWhat is Conveyance?Mannings Equation:Q = K Sf 1/2Conveyance K is:K = (1.486/n) A R2/3

Conveyance CalculationsHEC-RAS Default Method

Computational ProcedureWater Surface Guess1. The first guess of the water surface: downstream depth projected onto upstream cross section.2. Second guess: WSnew = WSassumed + 0.7 (WScomputed - WSassumed)3. Subsequent Trials: Secant projection method4. If secant method fails: WSnew = (WSassumed + WScomputed) / 2

Computational ProcedureTolerances and TrialsDefault tolerances and trial settings:- Water surface calculation tolerance = 0.01 ft (0.0001 - 0.1)- Maximum difference tolerance = 0.3 ft (0.1 - 1.0)- Maximum number of iterations = 20 trials (3 - 40)What happens if there is no convergence after 20 trials?- If 0.01 < minimum error < 0.3 ft, then use water surface with minimum error.- If minimum error >= 0.3 ft, then default to critical depth.

Note: Minimum error is the error associated with the best guess of the water surface during the 20 trials.

Critical Depth DeterminationCritical Depth will be computed for a cross section if any of the following conditions are satisfied:

Program could not balance the energy equation within specified tolerance and number of trials.

Calculated water surface is close to critical depth.

Supercritical flow regime is being calculated.

Cross section is an external boundary section.

User requested critical depth as an output option.

Critical Depth DeterminationCritical depth is found by computing minimum specific energy.HEC-RAS has two methods for computing critical depth.Parabolic Method - built for speedSlicing Method - built for accuracy

Critical Depth - ProcedureProgram uses Parabolic Method by DefaultThis can be changed to the Slicing method

Program automatically switches to slicing method if any of the following occur:Parabolic method fails to get answer within toleranceParabolic answer is at or near top of levee or ineffective flow area

Critical Depth - Local Minimum

Momentum Equation

Momentum EquationP2 - P1 + Wx - Ff = Q p VxWhere: P = Hydrostatic Pressure Wx = Force due to weight of water in x-directionFf = Force due to external friction from 2 to 1Q = Dischargep = Density of water Vx = Change in velocity from 2 to 1 in x-direction

Momentum Equation - ForcesPressure:Weight:Friction:Where:Mass x acceleration:

Momentum EquationThe momentum equation and principles are used in HEC-RAS for the following:Mixed flow regime calculations - locating hydraulic jumpsLow flow bridge hydraulicsStream junction analysis - optional method

Cross Section SpacingCross sections should be placed at representative locations to describe the changes in geometry.Additional cross sections should be added at locations where changes occur in discharge, slope, velocity, and roughness.Cross sections must also be added at levees, bridges, culverts, and other structures.

Cross Section Spacing - SlopeBed slope plays an important role in cross section spacing.Steeper slopes require more cross sectionsStreams flowing under supercritical flow may require cross sections on the order of 50 feet or less.Larger uniform rivers with flat slopes may only require cross sections on the order of 1000 ft or less.

Cross Section Spacing -How do you know if you have enough sections? Use the HEC-RAS cross section interpolation.Make a new plan and run the model.Compare before and after results

Model LimitationsLimitations of the One-Dimensional energy equation:Flow is steady with respect to time.Flow is gradually varied with respect to distance.Dominant forces are in the X-direction.Channel slopes should be less than 1:10.Other limitationsReal world flows are unsteadyReal world flows are not 1-D flow but 3-D

RecapIn this lecture we reviewed:Data required for river models1-D steady flow river analysisLimitations of the 1-D approachHEC-RAS input and outputSteady flow RAS applications

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