Overview of CFD Verification and Validation

Introduction

This page presents an overview of the process of the verification and validation of computational fluid dynamics (CFD) simulations. The overall objective is to demonstrate the accuracy of CFD codes so that they may be used with confidence for aerodynamic simulation and that the results be considered credible for decision making in design.

One should first understand the distinctions between a code, simulation, and model. The formal definitions of these terms are defined on the page entitled Glossary of Verification and Validation Terms. Essentially, one implements a model into a computer code and then uses the code to perform a CFD simulation which yield values used in the engineering analysis. Verification and validation examines the errors in the code and simulation results.

Credibility is obtained by demonstrating acceptable levels of uncertainty and error. A discussion of the uncertainties and errors in CFD simulations is provided on the page entitled Uncertainty and Error in CFD Simulations. The levels of uncertainties and errors are determined through verification assessment and validation assessment.

Verification assessment determines if the programming and computational implementation of the conceptual model is correct. It examines the mathematics in the models through comparison to exact analytical results. Verification assessment examines for computer programming errors.

Validation assessment determines if the computational simulation agrees with physical reality. It examines the science in the models through comparison to experimental results.

There is professional disagreement on exact procedures for verification and validation of CFD simulations. CFD is maturing, but still an emerging technology. CFD is a complex technology involving strongly coupled non-linear partial differential equations which attempt to computationally model theoretical and experimental models in a discrete domain of complex geometric shape. A detailed assessment of errors and uncertainties has to concern itself with the three roots of CFD: theory, experiment, and computation. Further, the application of CFD is rapidly expanding with the growth in computational resources. In this work, we primarily follow the verification and validation guidelines established by the AIAA [AIAA-G-077-1998]. Note that this is a guide - no standards yet exist for CFD simulation verification and validation. Other ideas from other researchers in this discipline will also be included. Their papers are referenced in the bibliography. Notable among them is the book on verification and validation published by Roache.

Verification and validation are on-going activities due to the complex nature of the CFD codes and expanding range of possible applications. Some basic verfication should be done prior to release of a code and basic validation studies should be performed on classes of flow features prior to use of the code for similar flows. However, as the code continues to develop, verification and validation should continue.

Use of CFD Results

The level of accuracy required from a CFD analysis depends on the desired use of the results. A conceptual design effort may be content with general shock structure information, whereas a detailed design may require accurate determination of the pressure recovery. Each quantity to be determined generally has its own accuracy requirement. Levels of credibility may vary according to the information required.

The application of CFD for design and analysis may be catagorized into three levels according to increased levels of required accuracy: 1) provide qualitative information, 2) provide incremental quantities, and 3) provide absolute quantities. This discussion follows the ideas of Benek et al.

Provide qualitative information. CFD provides details on the entire flow field not possible with experimental methods. This is useful in understanding on a qualitative level the behavior of the flow field. Accuracy requirements are low.

Provide incremental quantities. Corrections to experimental observations can be provided by CFD at a higher accuracy than existing with the CFD method. This is due to cancellation of part of the error when taking the differences. For example, if there is a design change from a baseline, for which the quanity is known, P_baseline, the quantity P for the design change can be expressed as:

P = P_baseline + dP

where dP is the increment in P corresponding to the design change. If two CFD simulations are performed, the first with the baseline geometry and the second with the modified geometry, then the increment in P due to the modified geometry can be estimated as,

dP = ( P + E )₂ - ( P + E )₁ = dP_actual + dE.

The E is the error associated with the quantity P obtained from the CFD simulation. As can be seen, the error to the increment is dE, which cancels out some of the error.

Provide absolute quantities. This level involves determining absolute values of the quantity P and requires the highest level of accuracy. The accuracy required is usually stated as part of the design process. The accuracy observed from the CFD simulation varies according to the character of the quantity, and so, it is not possible to state an accuracy or error band that applies to all quantities obtained from the CFD simulation. The verification methods discussed below regarding a grid convergence study will provide the error band for the calculations.

Flow Characteristics

In applying CFD for flows typical of aerospace systems, we must first understand the characteristics of the flow. We must understand the reality upon which we will validate the CFD code and processes.

The flow is characterized primarily by the Mach number. We are interested in analyzing flows spanning the Mach number range from Mach 0 (static conditions) to 25 (access to space).

The flow is characterized by high Reynolds numbers which result in regions of laminar flow transitioning to turbulent flow. Flows along the body and inlet surfaces create boundary layers. Adverse pressure gradient may be present for internal flows. At transonic, supersonic, and hypersonic speeds, shock waves are present. Under these conditions, the boundary layer may separate.

At hypersonic Mach numbers, real gas effects may become important. This requires use of chemistry models for calorically and thermally perfect gases, equilibrium air, and chemically reaction of gas mixtures.

Often the geometry of the system is complex, which has to be physically modeled.

Unsteady flow may become important.

Physical Models

There are several physical models that are commonly used within CFD codes:

Spatial Dimension. The geometry of the inlet may be modelled in some cases using two-dimensional or axisymmetric space rather than full three-dimensional.

Temporal Dimension. One may assume steady-state flow or attempt to capture the time variations.

Navier-Stokes Equations. The Navier-Stokes equations govern the continuum flow. Viscous and heat conduction effects are modelled. If these are removed, then inviscid flow can be used.

Turbulence Models. Various algebraic, one-equation, and two-equation turbulence models exist with various parameters and freestream boundary conditions. The option of wall functions exists.

Thermodynamic and Transport Properties. Constants and relations for thermodynamic and transport properties are generally constants, algebraic equations, or curve fits.

Air Chemistry Models. Inlet flows typically involve calorically perfect air adequately described by the perfect gas equation of state. At higher temperatures (greater than 700K), modeling of thermally perfect air, equilibrium air, and chemically reacting air (temperatures greater than 2000 K) may be needed.

Flow Boundary Conditions. These include subsonic and supersonic freestream inflow and outflow. Also inflow and outflow of plenum chambers.

Bleed / Blowing. These can be treated as boundary conditions as a mass flow or porous boundary. Another option is to grid the slots and holes of the actual geometry.

Flow Control Devices. Flow control is important and several new technologies have developed. Vortex generators are the primary flow control devices used in inlets. These can be modeled or an approximation of the geometry can be gridded.